This document outlines 54 tutorials that provide examples of constructing tables and graphs for exponential functions of various bases (2, 10, e) and characteristics of the coefficients a and b. Each tutorial works through an example of an exponential function of the form y = a*b^x, varying the values of a and b to illustrate different patterns in the table and graph.
Tutorials--Logarithmic Functions in Tabular and Graph Form Media4math
This document contains 120 examples of tutorials that construct function tables and graphs for logarithmic functions in tabular and graph form. The tutorials vary the base of the logarithm (base 10 or base 2), the characteristics of the logarithmic function (values of a, b, c for the function y = log(ax + b) + c), and whether the function has a single logarithm or a scaled logarithm (with coefficient d).
Tutorials--Cube Root Functions in Tabular and Graph Form Media4math
This document provides 40 examples of tutorials that construct function tables and graphs for cube root functions of the form y=cuberoot(ax+b)+c. Each tutorial varies the values of a, b, and c to illustrate different forms of cube root functions.
Tutorials--Secant Functions in Tabular and Graph Form Media4math
This document describes 65 tutorials that provide examples of constructing tables and graphs for secant functions of the form y = sec(ax + b) + c, where a, b, and c can have various values. Each tutorial examines a different combination of values for a, b, and c to demonstrate secant functions with different periodic behaviors and shifts.
Tutorials--Sine Functions in Tabular and Graph Form Media4math
This document describes 65 tutorials that provide examples of constructing tables and graphs for sine functions of the form y = a*sin(bx + c) + d, with varying values for the coefficients a, b, c, and d. Each tutorial works through an example with different coefficient values to demonstrate how to represent sine functions in tabular and graphical form for different periodic behaviors and vertical and horizontal shifts.
Tutorials--Tangent Functions in Tabular and Graph FormMedia4math
This document provides 65 examples of tutorials that construct function tables and graphs for tangent functions of the form y = tan(ax + b) + c. Each tutorial varies the values of a, b, and c to illustrate different characteristics of tangent graphs.
Tutorials--Square Root Functions in Tabular and Graph Form Media4math
This document provides 40 examples of tutorials for constructing tables and graphs of square root functions. Each tutorial examines a square root function of the form y = sqrt(ax + b) + c or y = d * sqrt(ax + b) + c, varying the values of a, b, c, and d to demonstrate different forms of square root functions.
Tutorials--Cosine Functions in Tabular and Graph Form Media4math
This document describes 65 tutorials on constructing tables and graphs for cosine functions of the form y=cos(ax+b). Each tutorial varies the values of a and b to demonstrate different characteristics of the cosine function graphed and tabulated over changing domains. The tutorials cover different positive, negative, and fractional values of a and various phase shifts introduced by changing the value of b.
Tutorials--Cosecant Functions in Tabular and Graph FormMedia4math
This document describes 65 tutorials that provide examples of constructing tables and graphs for cosecant functions. Each tutorial examines a cosecant function of the form y = csc(ax + b) or y = a * csc(bx + c) + d with different values for the variables a, b, c, and d. The tutorials demonstrate how changing the values of these variables affects the shape of the cosecant function graph and its table of values.
Tutorials--Logarithmic Functions in Tabular and Graph Form Media4math
This document contains 120 examples of tutorials that construct function tables and graphs for logarithmic functions in tabular and graph form. The tutorials vary the base of the logarithm (base 10 or base 2), the characteristics of the logarithmic function (values of a, b, c for the function y = log(ax + b) + c), and whether the function has a single logarithm or a scaled logarithm (with coefficient d).
Tutorials--Cube Root Functions in Tabular and Graph Form Media4math
This document provides 40 examples of tutorials that construct function tables and graphs for cube root functions of the form y=cuberoot(ax+b)+c. Each tutorial varies the values of a, b, and c to illustrate different forms of cube root functions.
Tutorials--Secant Functions in Tabular and Graph Form Media4math
This document describes 65 tutorials that provide examples of constructing tables and graphs for secant functions of the form y = sec(ax + b) + c, where a, b, and c can have various values. Each tutorial examines a different combination of values for a, b, and c to demonstrate secant functions with different periodic behaviors and shifts.
Tutorials--Sine Functions in Tabular and Graph Form Media4math
This document describes 65 tutorials that provide examples of constructing tables and graphs for sine functions of the form y = a*sin(bx + c) + d, with varying values for the coefficients a, b, c, and d. Each tutorial works through an example with different coefficient values to demonstrate how to represent sine functions in tabular and graphical form for different periodic behaviors and vertical and horizontal shifts.
Tutorials--Tangent Functions in Tabular and Graph FormMedia4math
This document provides 65 examples of tutorials that construct function tables and graphs for tangent functions of the form y = tan(ax + b) + c. Each tutorial varies the values of a, b, and c to illustrate different characteristics of tangent graphs.
Tutorials--Square Root Functions in Tabular and Graph Form Media4math
This document provides 40 examples of tutorials for constructing tables and graphs of square root functions. Each tutorial examines a square root function of the form y = sqrt(ax + b) + c or y = d * sqrt(ax + b) + c, varying the values of a, b, c, and d to demonstrate different forms of square root functions.
Tutorials--Cosine Functions in Tabular and Graph Form Media4math
This document describes 65 tutorials on constructing tables and graphs for cosine functions of the form y=cos(ax+b). Each tutorial varies the values of a and b to demonstrate different characteristics of the cosine function graphed and tabulated over changing domains. The tutorials cover different positive, negative, and fractional values of a and various phase shifts introduced by changing the value of b.
Tutorials--Cosecant Functions in Tabular and Graph FormMedia4math
This document describes 65 tutorials that provide examples of constructing tables and graphs for cosecant functions. Each tutorial examines a cosecant function of the form y = csc(ax + b) or y = a * csc(bx + c) + d with different values for the variables a, b, c, and d. The tutorials demonstrate how changing the values of these variables affects the shape of the cosecant function graph and its table of values.
The document defines exponential functions as functions of the form f(x) = ax, where a is the base and a > 0, a ≠ 1. Exponential functions with bases greater than 1 have graphs that increase rapidly and have a horizontal asymptote of y = 0. Exponential functions with bases between 0 and 1 have graphs that increase more slowly and also have a horizontal asymptote of y = 0. Examples are given of sketching the graphs of various exponential functions, including translations and reflections of f(x) = 2x. The irrational number e, which is approximately 2.718, is important in applications involving growth and decay.
2.2 exponential function and compound interestmath123c
The document discusses exponential functions and their properties. It defines exponential functions as functions of the form f(x) = bx where b > 0 and b ≠ 1. Some key points made in the document include:
- The rules for exponents such as b0, b-k, (√b)k, and (b1/k) are explained.
- Exponential functions are defined for all real numbers x.
- Examples are provided to illustrate calculating exponential expressions and functions with integer, fractional, decimal, and real-number exponents.
- Exponential functions appear in various fields like finance, science, and engineering. Common exponential functions mentioned are y = 10x, y = ex, and y
This document defines common (base 10) and natural (base e) logarithms and explains how to evaluate, solve equations involving, and graph logarithmic functions. It also discusses important properties of logarithms including:
- Logarithms are the inverse functions of exponentials.
- The natural logarithm ln(x) is the logarithm with base e, where e is an important mathematical constant approximately equal to 2.718.
- The domain of ln(x) is x > 0, since it is undefined for non-positive values. The range extends from -∞ to ∞.
This document provides information about simple interest, including its meaning, formula, and examples. Simple interest is interest computed only on the principal amount and not on accumulated interest from prior periods. The formula for simple interest is: SI = Principal x Rate x Time / 100. Three examples demonstrate calculating simple interest using different principal amounts, interest rates, and time periods. The document concludes with two homework questions applying the simple interest formula.
This document contrasts linear and exponential functions. Linear functions increase at a constant rate, while exponential functions increase at a changing rate but at a constant percent rate. An example compares two job offers, one with linear growth and one exponential. Exponential growth is also modeled using compound interest in a savings account. The growth factor is introduced to write the compound interest formula in a simpler way. Exponential decay is demonstrated using a medication example where the amount in the bloodstream decreases by 15% each hour. Finally, general properties and graphs of exponential functions are reviewed.
The document defines exponential functions as functions of the form f(x) = bx, where b is a positive constant other than 1. It discusses how the graph of an exponential function depends on whether b is greater than or less than 1. Specifically, if b > 1 the graph increases to the right, and if 0 < b < 1 the graph decreases to the right. The document also covers transformations of exponential functions, including vertical and horizontal shifting, reflecting, and stretching/shrinking. It introduces the special number e, defines it as the limit of (1 + 1/n)n as n approaches infinity, and discusses its role in compound interest formulas.
Logarithms were originally developed to simplify complex arithmetic calculations by transforming multiplication into addition. A logarithm relates an exponential equation to its logarithmic form and vice versa. The key property of logarithms is that they allow rewriting exponential equations as logarithmic expressions and vice versa. This property is important for solving exponential equations. Logarithmic expressions are undefined if the argument is negative.
The document reviews the basics of exponential notation. It defines AN as A multiplied by itself N times, with A as the base and N as the exponent. The rules of exponents are then presented, including the multiplication, division, power, negative, fractional, and decimal exponent rules. Examples are provided to demonstrate simplifying expressions using these rules.
This document discusses the properties and laws of logarithms. It explains that common and natural logarithms have the same properties and laws, even though their bases differ. The key properties covered include: logarithms are only defined for positive values; ln1=0, ln e=1; and the product, quotient, and power laws. Several examples are worked through to demonstrate how to use these properties and laws to simplify logarithmic expressions and solve equations. The document emphasizes that understanding logarithmic properties and how to manipulate logarithms is important for advanced math, science, and engineering courses.
This document provides an overview of exponential functions including:
- Definitions of exponential functions for positive integer, rational, and irrational exponents. Conventions are established to define exponents for all real number bases and exponents.
- Properties of exponential functions including that they are continuous functions with domain of all real numbers and range from 0 to infinity. Properties involving addition, subtraction, multiplication, and division of exponents are proven.
- Examples are provided to demonstrate simplifying expressions using properties of exponents, including fractional exponents.
Compound interest is interest calculated on both the principal amount and on any interest that has already been earned over multiple periods. It is usually used for loans of more than one year. Compound interest is higher than simple interest because the interest earns interest. The compound interest formula can be used to calculate the future value (FV) of an investment given the present value (PV), interest rate per period (i), and number of compounding periods (n). An example calculates that $1500 compounded quarterly at 6.75% annually for 10 years results in a future value of $2929.
Krish wants to buy a house for Rs. 30,00,000 but does not have enough savings, so he must take out a loan. A loan is money borrowed from a lender like a bank that must be paid back with additional interest. Simple interest is calculated using the principal amount, interest rate, and time period, with the formula: Simple Interest = Principal * Rate * Time / 100. The document provides examples of calculating simple interest on various loans to explain the concept.
The document defines logarithmic functions and provides examples of converting between logarithmic and exponential forms. It discusses the properties of logarithmic equality and solving logarithmic equations by rewriting them in exponential form. Key points include: logarithmic and exponential forms are inverses; the exponent becomes the logarithm; logarithmic functions have a domain of positive real numbers; and solving logarithms involves setting arguments equal when bases are the same.
The document discusses exponential functions and exponential equations. Exponential functions have the form f(x) = bx, where b is the base and x is the exponent. These functions are important in modeling real-world phenomena like population growth. Exponential equations set the exponents of the same base equal to solve for the variable. They can be solved by rewriting all terms to have the same base, setting the exponents equal, and solving the resulting equation.
An exponential function has the form y = a · bx, where a and b are constants and b must be greater than 0. This document discusses exponential functions through examples and explanations. It explores how changing the constants a and b impact the graph of the function. It also introduces the equality property of exponential functions, which states that if the bases are the same, the exponents can be set equal to solve equations. Several examples demonstrate how to use this property to solve equations involving exponential functions.
This document discusses properties of logarithms, including:
1) Logarithms with the same base "undo" each other according to the inverse function relationship between logarithms and exponents.
2) Logarithmic expressions can be expanded using properties to write them as sums or differences of individual logarithmic terms, or condensed into a single logarithm.
3) The change of base formula allows converting between logarithms with different bases, with common uses being to change to base 10 or the base of natural logarithms.
The document explains compound interest, how it is calculated, and provides examples. Compound interest is interest paid on both the principal amount and accumulated interest over time. It is commonly used in savings accounts and works by compounding interest periodically, such as daily, quarterly, or annually. The document shows how to use a compound interest table to calculate the balance and interest earned for various principal amounts over different time periods at given interest rates that are compounded periodically.
This document discusses exponential functions. It defines exponential functions as functions where f(x) = ax + B, where a is a real constant and B is any expression. Examples of exponential functions given are f(x) = e-x - 1 and f(x) = 2x. The document also discusses evaluating exponential equations with like and different bases using logarithms. It provides examples of graphing exponential functions and discusses the key characteristics of functions of the form f(x) = bx, including their domains, ranges, and asymptotic behavior. The document concludes with an example of applying exponential functions to model compound interest.
1) The document discusses graphing and properties of exponential and logarithmic functions, including: graphing exponential functions by substituting values of the variable into the equation, graphing logarithmic functions using the change of base formula, and properties like the product, quotient, and power properties of logarithms.
2) Examples are provided of solving exponential and logarithmic equations using properties like changing bases to the same value, multiplying or dividing arguments using the product and quotient properties, and applying exponents using the power property.
3) Steps shown include using properties to isolate the variable, set arguments or exponents equal to each other, and solve the resulting equation.
Tutorials--Absolute Value Functions in Tabular and Graph Form Media4math
This document provides 40 examples of tutorials for constructing tables and graphs of absolute value functions. Each tutorial examines a different form of the absolute value function y = |ax + b| + c with varying values for the coefficients a, b, c, and d. The tutorials explore all possible combinations of coefficient values.
Tutorials--Rational Functions in Tabular and Graph FormMedia4math
This document provides 28 tutorials that construct function tables and graphs for rational functions of the form f(x) = a/(bx + c) + d, where a, b, c, and d are varied constants. Each tutorial works through an example of representing a rational function in both tabular and graphical form.
The document defines exponential functions as functions of the form f(x) = ax, where a is the base and a > 0, a ≠ 1. Exponential functions with bases greater than 1 have graphs that increase rapidly and have a horizontal asymptote of y = 0. Exponential functions with bases between 0 and 1 have graphs that increase more slowly and also have a horizontal asymptote of y = 0. Examples are given of sketching the graphs of various exponential functions, including translations and reflections of f(x) = 2x. The irrational number e, which is approximately 2.718, is important in applications involving growth and decay.
2.2 exponential function and compound interestmath123c
The document discusses exponential functions and their properties. It defines exponential functions as functions of the form f(x) = bx where b > 0 and b ≠ 1. Some key points made in the document include:
- The rules for exponents such as b0, b-k, (√b)k, and (b1/k) are explained.
- Exponential functions are defined for all real numbers x.
- Examples are provided to illustrate calculating exponential expressions and functions with integer, fractional, decimal, and real-number exponents.
- Exponential functions appear in various fields like finance, science, and engineering. Common exponential functions mentioned are y = 10x, y = ex, and y
This document defines common (base 10) and natural (base e) logarithms and explains how to evaluate, solve equations involving, and graph logarithmic functions. It also discusses important properties of logarithms including:
- Logarithms are the inverse functions of exponentials.
- The natural logarithm ln(x) is the logarithm with base e, where e is an important mathematical constant approximately equal to 2.718.
- The domain of ln(x) is x > 0, since it is undefined for non-positive values. The range extends from -∞ to ∞.
This document provides information about simple interest, including its meaning, formula, and examples. Simple interest is interest computed only on the principal amount and not on accumulated interest from prior periods. The formula for simple interest is: SI = Principal x Rate x Time / 100. Three examples demonstrate calculating simple interest using different principal amounts, interest rates, and time periods. The document concludes with two homework questions applying the simple interest formula.
This document contrasts linear and exponential functions. Linear functions increase at a constant rate, while exponential functions increase at a changing rate but at a constant percent rate. An example compares two job offers, one with linear growth and one exponential. Exponential growth is also modeled using compound interest in a savings account. The growth factor is introduced to write the compound interest formula in a simpler way. Exponential decay is demonstrated using a medication example where the amount in the bloodstream decreases by 15% each hour. Finally, general properties and graphs of exponential functions are reviewed.
The document defines exponential functions as functions of the form f(x) = bx, where b is a positive constant other than 1. It discusses how the graph of an exponential function depends on whether b is greater than or less than 1. Specifically, if b > 1 the graph increases to the right, and if 0 < b < 1 the graph decreases to the right. The document also covers transformations of exponential functions, including vertical and horizontal shifting, reflecting, and stretching/shrinking. It introduces the special number e, defines it as the limit of (1 + 1/n)n as n approaches infinity, and discusses its role in compound interest formulas.
Logarithms were originally developed to simplify complex arithmetic calculations by transforming multiplication into addition. A logarithm relates an exponential equation to its logarithmic form and vice versa. The key property of logarithms is that they allow rewriting exponential equations as logarithmic expressions and vice versa. This property is important for solving exponential equations. Logarithmic expressions are undefined if the argument is negative.
The document reviews the basics of exponential notation. It defines AN as A multiplied by itself N times, with A as the base and N as the exponent. The rules of exponents are then presented, including the multiplication, division, power, negative, fractional, and decimal exponent rules. Examples are provided to demonstrate simplifying expressions using these rules.
This document discusses the properties and laws of logarithms. It explains that common and natural logarithms have the same properties and laws, even though their bases differ. The key properties covered include: logarithms are only defined for positive values; ln1=0, ln e=1; and the product, quotient, and power laws. Several examples are worked through to demonstrate how to use these properties and laws to simplify logarithmic expressions and solve equations. The document emphasizes that understanding logarithmic properties and how to manipulate logarithms is important for advanced math, science, and engineering courses.
This document provides an overview of exponential functions including:
- Definitions of exponential functions for positive integer, rational, and irrational exponents. Conventions are established to define exponents for all real number bases and exponents.
- Properties of exponential functions including that they are continuous functions with domain of all real numbers and range from 0 to infinity. Properties involving addition, subtraction, multiplication, and division of exponents are proven.
- Examples are provided to demonstrate simplifying expressions using properties of exponents, including fractional exponents.
Compound interest is interest calculated on both the principal amount and on any interest that has already been earned over multiple periods. It is usually used for loans of more than one year. Compound interest is higher than simple interest because the interest earns interest. The compound interest formula can be used to calculate the future value (FV) of an investment given the present value (PV), interest rate per period (i), and number of compounding periods (n). An example calculates that $1500 compounded quarterly at 6.75% annually for 10 years results in a future value of $2929.
Krish wants to buy a house for Rs. 30,00,000 but does not have enough savings, so he must take out a loan. A loan is money borrowed from a lender like a bank that must be paid back with additional interest. Simple interest is calculated using the principal amount, interest rate, and time period, with the formula: Simple Interest = Principal * Rate * Time / 100. The document provides examples of calculating simple interest on various loans to explain the concept.
The document defines logarithmic functions and provides examples of converting between logarithmic and exponential forms. It discusses the properties of logarithmic equality and solving logarithmic equations by rewriting them in exponential form. Key points include: logarithmic and exponential forms are inverses; the exponent becomes the logarithm; logarithmic functions have a domain of positive real numbers; and solving logarithms involves setting arguments equal when bases are the same.
The document discusses exponential functions and exponential equations. Exponential functions have the form f(x) = bx, where b is the base and x is the exponent. These functions are important in modeling real-world phenomena like population growth. Exponential equations set the exponents of the same base equal to solve for the variable. They can be solved by rewriting all terms to have the same base, setting the exponents equal, and solving the resulting equation.
An exponential function has the form y = a · bx, where a and b are constants and b must be greater than 0. This document discusses exponential functions through examples and explanations. It explores how changing the constants a and b impact the graph of the function. It also introduces the equality property of exponential functions, which states that if the bases are the same, the exponents can be set equal to solve equations. Several examples demonstrate how to use this property to solve equations involving exponential functions.
This document discusses properties of logarithms, including:
1) Logarithms with the same base "undo" each other according to the inverse function relationship between logarithms and exponents.
2) Logarithmic expressions can be expanded using properties to write them as sums or differences of individual logarithmic terms, or condensed into a single logarithm.
3) The change of base formula allows converting between logarithms with different bases, with common uses being to change to base 10 or the base of natural logarithms.
The document explains compound interest, how it is calculated, and provides examples. Compound interest is interest paid on both the principal amount and accumulated interest over time. It is commonly used in savings accounts and works by compounding interest periodically, such as daily, quarterly, or annually. The document shows how to use a compound interest table to calculate the balance and interest earned for various principal amounts over different time periods at given interest rates that are compounded periodically.
This document discusses exponential functions. It defines exponential functions as functions where f(x) = ax + B, where a is a real constant and B is any expression. Examples of exponential functions given are f(x) = e-x - 1 and f(x) = 2x. The document also discusses evaluating exponential equations with like and different bases using logarithms. It provides examples of graphing exponential functions and discusses the key characteristics of functions of the form f(x) = bx, including their domains, ranges, and asymptotic behavior. The document concludes with an example of applying exponential functions to model compound interest.
1) The document discusses graphing and properties of exponential and logarithmic functions, including: graphing exponential functions by substituting values of the variable into the equation, graphing logarithmic functions using the change of base formula, and properties like the product, quotient, and power properties of logarithms.
2) Examples are provided of solving exponential and logarithmic equations using properties like changing bases to the same value, multiplying or dividing arguments using the product and quotient properties, and applying exponents using the power property.
3) Steps shown include using properties to isolate the variable, set arguments or exponents equal to each other, and solve the resulting equation.
Tutorials--Absolute Value Functions in Tabular and Graph Form Media4math
This document provides 40 examples of tutorials for constructing tables and graphs of absolute value functions. Each tutorial examines a different form of the absolute value function y = |ax + b| + c with varying values for the coefficients a, b, c, and d. The tutorials explore all possible combinations of coefficient values.
Tutorials--Rational Functions in Tabular and Graph FormMedia4math
This document provides 28 tutorials that construct function tables and graphs for rational functions of the form f(x) = a/(bx + c) + d, where a, b, c, and d are varied constants. Each tutorial works through an example of representing a rational function in both tabular and graphical form.
Tutorials--Quadratic Functions in Tabular and Graphic FormMedia4math
This document provides 37 examples of tutorials that construct function tables and graphs for quadratic functions in standard form with varying characteristics for the coefficients a, b, and c. Each tutorial example uses a different combination of positive, negative, and zero values for the coefficients to illustrate different forms of quadratic functions.
Tutorials: Graphs of Quadratic Functions in Standard FormMedia4math
This document outlines 18 examples of graphs of quadratic functions in standard form. The examples systematically vary the parameters a, b, and c to demonstrate how changing these parameters affects the shape and position of the graph of the quadratic function. Specifically, it explores how the graph is impacted when a, b, and c are positive versus negative values, as well as when they are equal to zero.
1. The document provides teaching materials for a lesson on quadratic functions in the form y = ax^2 + bx + k. It includes a teachers' guide, lesson plan, and student worksheet.
2. The teachers' guide provides instructions for setting up the lesson using a spreadsheet to demonstrate different quadratic graphs. It explains how to input data and plot graphs to show how the graph changes as the values of a, b, and k are varied.
3. The lesson plan is for a double period and includes introducing the topic with examples, having students work in groups to observe graph changes, determining the vertex, and applying it to a real-world problem. The student worksheet has corresponding activities for students to
This document provides instructions on how to evaluate algebraic expressions using a Casio fx-350ES PLUS calculator. It includes an example of evaluating the expression a2+b3 when a=4 and b=2. The steps shown are to assign the values 4 and 2 to the variables a and b using the calculator's storage function, then using the variables to calculate the expression. Exercises are provided to evaluate other algebraic expressions using the given calculator.
This document provides instructions on how to evaluate algebraic expressions using a Casio fx-350ES PLUS calculator. It includes an example of evaluating the expression a2+b3 when a=4 and b=2. The steps shown are to assign the values 4 and 2 to the variables a and b using the calculator's storage function, then using the variables to calculate the expression. Exercises are provided to evaluate other algebraic expressions using the given calculator.
The document discusses quadratic functions, including how to recognize a quadratic function based on its standard form, how to plot graphs of quadratic functions based on either tabulated values or a given function, and examples of determining if a function is quadratic and plotting quadratic graphs. Key aspects covered are the standard form of a quadratic function as f(x) = ax^2 + bx + c where a ≠ 0, recognizing quadratic functions, tabulating x and f(x) values for a given quadratic function, and using Geometer's Sketchpad software to plot the graphs.
Here are the key steps to solve this problem algebraically:
Let x = number of units of product X
Let y = number of units of product Y
Write equations relating the process hours to the number of units:
3x + 2x = Hours used in A
1y + 4y = Hours used in B
Solve the simultaneous equations to find the maximum number of each product that can be made.
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
This document discusses Bézier curves and their properties. It begins by stating that traditional parametric curves are not very geometric and do not provide intuitive shape control. It then outlines desirable properties for curve design systems, including being intuitive, flexible, easy to use, providing a unified approach for different curve types, and producing invariant curves under transformations. The document proceeds to discuss Bézier, B-spline and NURBS curves which address these properties by allowing users to manipulate control points to modify curve shapes. Key properties of Bézier curves are described, including their basis functions and the fact that moving control points modifies the curve smoothly. Cubic Bézier curves are discussed in detail as a common parametric curve type, and
Here are the key steps to solve this problem algebraically:
Let x = number of units of product X
Let y = number of units of product Y
Equation for process A: 3x + y ≤ 1750
Equation for process B: 2x + 4y ≤ 4000
Solve the two equations simultaneously using elimination:
3x + y = 1750
2x + 4y = 4000
Eliminate y by subtracting the equations:
x = 1250
Substitute x = 1250 into one of the original equations to find y:
3(1250) + y = 1750
y = 500
Therefore, the maximum number of units of X is 1250 and
This lesson plan teaches students how to graph linear functions using x-intercepts and y-intercepts. It includes the following:
1) An activity where students name local products on a graph and connect points to form lines representing stores.
2) An explanation of how two points determine a line and how linear equations can be graphed using intercepts. Students practice finding the intercepts of an example equation.
3) An application where students graph equations using given intercepts and an assessment where they graph additional equations and find intercepts of other equations.
MODULE 5 QuizQuestion1. Find the domain of the function. E.docxmoirarandell
MODULE 5 Quiz
Question
1.
Find the domain of the function. Express your answer in interval notation.
a.
b.
c.
d.
2.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
3.
Graph f(x) = |x – 1|.
a.
b.
c.
d.
4.
Determine whether the function is even, odd, or neither. f(x) = x5 + 4
a. Even
b. Odd
c. Neither
5.
Find the value of f(3) if f(x) = 4x2 + x.
a. 38
b. 39
c. 40
d. 41
6.
Use the graph of the function to estimate: (a) f(–6), (b) f(1), (c) All x such that f(x) = 3
a. (a) 4 (b) 3 (c) –5, 1
b. (a) 5 (b) 4 (c) –3, 1
c. (a) 1 (b) 2 (c) –5, 2
d. (a) 7 (b) 5 (c) –5, 6
7.
The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g. The graph of is horizontally stretched by a factor of 0.1, reflected in the y axis, and shifted four units to the left.
a.
b.
c.
d.
8.
Evaluate f(–1).
a. –1
b. 8
c. 0
d. –2
9.
Determine whether the function is even, odd, or neither. f(x) = x3 – 10x
a. Even
b. Odd
c. Neither
10.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
11.
Determine whether the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y. x|y| = x + 5
a. A function with domain all real numbers
b. A function with domain all real numbers except 0
c. Not a function: when x = 0, y = ±5
d. Not a function: when x = 1, y = ±6
12.
Graph y = (x – 2)2 + 1
a.
b.
c.
d.
13.
Find the y-intercept(s).
a. –2
b. 1, –3
c. –3
d. None
14.
Determine whether the correspondence defines a function. Let F be the set of all faculty teaching Chemistry 101 at a university, and let S be the set of all students taking that course. Students from set S correspond to their Chemistry 101 instructors.
a. A function
b. Not a function
15.
Determine whether the function is even, odd, or neither. f(x) = –4x2 + 5x + 3
a. Even
b. Odd
c. Neither
16.
Indicate whether the table defines a function.
a. Function
b. Not a function
17.
Use the graph of the function to estimate: (a) f(1), (b) f(–5),and (c) All x such that f(x) = 3
a. (a) –3 (b) –9 (c) 7
b. (a) –3 (b) –9 (c) –1
c. (a) 5 (b) –1 (c) 7
d. (a) 5 (b) –1 (c) –1
18.
Find the intervals over which f is increasing.
a. (–∞, –2], [1, ∞)
b. (–3, ∞)
c. (–∞, –3], [1, ∞)
d. None
19.
Evaluate f(4).
a. 4
b. 10
c. 5
d. –2
20.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
21.
Sketch the graph of the function f(x) = –2x + 3.
a.
b.
22.
Find the intervals over which f is decreasing.
a. (–∞, –2), [1, ∞)
b. (–∞, –2], [1, ∞)
c. (–∞, –3), [1, ∞)
d. (–∞, –3], [1, ∞)
23.
Indicate whether the table defines a function.
a. Function
b. Not a function
24.
Indicate whether the graph is the graph of a function.
a. ...
This document discusses the key elements of a quadratic function f(x) = ax^2 + bx + c. It explains that:
1) The y-intercept is indicated by the c coefficient as (0,c)
2) The vertex is calculated as (-b/2a, f(-b/2a))
3) The axis of symmetry passes through the vertex and is the line x=-b/2a.
It provides an example of the quadratic function f(x)=x^2+2x-8 and graphs it to illustrate these elements.
- The document discusses quadratic functions and their graphs. It explains that the graph of a quadratic function is a parabola, which is a U-shaped curve.
- It describes how to write quadratic functions in standard form and use that form to sketch the graph and find features like the vertex and axis of symmetry.
- Examples are provided to demonstrate how to graph quadratic functions in standard form and how to find the minimum or maximum value of a quadratic function by setting its derivative equal to zero.
This document provides 32 examples of solving one-step equations involving addition, subtraction, multiplication, and division. The examples cover equations with integer and decimal values where the unknown variable x is being solved for. Each example works through solving a different type of one-step equation, with the full set of examples addressing equations of the basic forms x ± a = b, a × x = b, and x ÷ a = b.
The document is about quadratic polynomial functions and contains the following information:
1. It discusses investigating relationships between numbers expressed in tables to represent them in the Cartesian plane, identifying patterns and creating conjectures to generalize and algebraically express this generalization, recognizing when this representation is a quadratic polynomial function of the type y = ax^2.
2. It provides examples of converting algebraic representations of quadratic polynomial functions into geometric representations in the Cartesian plane, distinguishing cases in which one variable is directly proportional to the square of the other, using or not using software or dynamic algebra and geometry applications.
3. It discusses characterizing the coefficients of quadratic functions, constructing their graphs in the Cartesian plane, and determining their zeros (
Mauricio opened a bank account with $20 and deposits $10 each week. His account balance can be modeled as a linear function f(x) = 20 + 10x, where x is the number of weeks and f(x) is the balance in dollars. The function shows that after 0 weeks the balance is $20, after 1 week it is $30, after 2 weeks $40, and so on, increasing by $10 each week.
This document discusses graphing quadratic functions. It provides three learning objectives: to graph quadratic functions, find the components of a quadratic function from its graph, and write quadratic functions in different forms. It then gives steps to calculate the axis of symmetry, vertex, x-intercepts, and y-intercepts of a quadratic function from its equation. Two examples are provided to demonstrate how to graph quadratic functions and find their key features from the equation. The last example solves a word problem about the maximum height of a basketball using a quadratic equation.
Ähnlich wie Tutorials--Exponential Functions in Tabular and Graph Form (20)
Geometric Construction: Creating a Teardrop ShapeMedia4math
Constructing a teardrop shape involves drawing three circles of different radii using a compass on graph paper. The teardrop shape is formed by the overlapping circular arcs from a radius 5 circle, another radius 5 circle, and a radius 3 circle. The overlapping arcs are highlighted and isolated by erasing the remaining circular areas to reveal the smooth teardrop curve created by the intersecting arcs.
A hands-on activity for explore a variety of math topics, including:
* Circumference and Diameter
* Linear functions and slope
* Ratios
* Data gathering and scatterplot
For more math resources, go to www.media4math.com.
Math in the News: Issue 111--Summer BlockbustersMedia4math
The document discusses summer blockbuster movies. Some key points:
- Summer is the peak movie season due to school being out and families looking for affordable entertainment options.
- Blockbusters are big-budget films released in the summer that draw huge audiences and make substantial profits. They typically feature recognizable stars, special effects, and family-friendly content.
- Examples of past summer blockbusters that fit this profile are provided.
- Data on the budget and earnings of Avatar, a highly successful blockbuster, show it had a budget of $425 million and grossed $760.5 million, resulting in a profit of $335.5 million.
This document advertises the digital math resources available through Media4Math, including over 11,000 resources that can be purchased individually or through a subscription. It provides information about the Marketplace, Open Educational Resource library, Worksheet library, and libraries of resources focused on teaching linear functions, quadratic functions, and other math topics through videos, games, and presentations.
Tutorials--The Language of Math--Variable Expressions--Multiplication and Sub...Media4math
This set of tutorials provides 32 examples of converting verbal expressions into variable expressions that involve multiplication and subtraction. Note: The download is a PPT file.
Tutorials--The Language of Math--Numerical Expressions--Multiplication Media4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve multiplication. Note: The download is a PPT file.
Tutorials--The Language of Math--Numerical Expressions--Division Media4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve division. Note: The download is a PPT file.
Tutorials--The Language of Math--Numerical Expressions--SubtractionMedia4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve subtraction. Note: The download is a PPT file.
Tutorials--Language of Math--Numerical Expressions--AdditionMedia4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve addition. The verbal expressions include these terms:
Plus
Increased by
In addition to
Added to
More than
This document discusses using mathematical models to represent the thawing of frozen turkeys. It introduces logarithmic functions as a model for thawing curves, as the temperature increases over time in a way similar to the inverse of an exponential cooling curve. The document provides guidelines from the USDA for safely thawing turkeys either in the refrigerator over several days or in a water container over several hours, and shows how to construct a logarithmic model to fit starting and ending temperature points for a turkey thawing in the refrigerator.
Tutorials: Linear Functions in Tabular and Graph FormMedia4math
This document provides 21 examples of linear functions presented as both tables and graphs. Each example shows a linear function in slope-intercept form with different characteristics for the slope and y-intercept, such as positive and negative slopes greater than, less than, and equal to 1, as well as zero slopes and various y-intercepts. The examples cover a range of linear functions demonstrated visually and numerically.
1. Jurassic World has become one of the highest grossing films worldwide and is ranked 7th on the global box office list.
2. Domestically, Jurassic World is ranked 5th on the North American box office top 10 list after only a few weeks.
3. The data shows domestic and international box office figures for the top 10 highest grossing films worldwide, with international sales making up a higher percentage for most films compared to domestic sales.
This document provides examples for solving two-step equations. It contains 32 examples that involve combinations of addition, subtraction, multiplication, and division, and show the steps to solve for the unknown using the inverse operations. The examples are divided into two sets - the first 16 have only positive numbers, while the remaining 16 can have positive or negative numbers.
This document outlines 26 tutorials that provide examples of finding the range of data sets containing various numbers of positive and negative integers. Each tutorial finds the range for a different data set size ranging from 8 to 20 numbers.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
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Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
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Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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2. Overview
This set of tutorials provides 54 examples of
exponential functions in tabular and graph form.
3. Tutorial--Exponential Functions in Tabular and Graph Form: Example 01. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: a = 1, b = 1.
4. Tutorial--Exponential Functions in Tabular and Graph Form: Example 02. In this
tutorial, construct a function table and graph for an exponential function of base
2 of the form y = a*2^(bx) with these characteristics: a > 1, b = 1.
5. Tutorial--Exponential Functions in Tabular and Graph Form: Example 03. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a = 1, b > 1.
6. Tutorial--Exponential Functions in Tabular and Graph Form: Example 04. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a > 1, b > 1.
7. Tutorial--Exponential Functions in Tabular and Graph Form: Example 05. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a = -1, b = -1.
8. Tutorial--Exponential Functions in Tabular and Graph Form: Example 06. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a < -1, b = -1.
9. Tutorial--Exponential Functions in Tabular and Graph Form: Example 07. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a = -1, b < -1.
10. Tutorial--Exponential Functions in Tabular and Graph Form: Example 08. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a < -1, b < -1.
11. Tutorial--Exponential Functions in Tabular and Graph Form: Example 09. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: -1 < a < 0, b = 1.
12. Tutorial--Exponential Functions in Tabular and Graph Form: Example 10. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: a = 1, -1 < b < 0.
13. Tutorial--Exponential Functions in Tabular and Graph Form: Example 11. In this
tutorial, construct a function table and graph for an exponential function of base
2 of the form y = a*2^(bx) with these characteristics: -1 < a < 0, -1 < b < 0.
14. Tutorial--Exponential Functions in Tabular and Graph Form: Example 12. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: -1 < a < 0, b = -1.
15. Tutorial--Exponential Functions in Tabular and Graph Form: Example 13. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: a = -1, -1 < b < 0.
16. Tutorial--Exponential Functions in Tabular and Graph Form: Example 14. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: 0 < a < 1, b = 1.
17. Tutorial--Exponential Functions in Tabular and Graph Form: Example 15. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a = 1, 0 < b < 1.
18. Tutorial--Exponential Functions in Tabular and Graph Form: Example 16. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: 0 < a < 1, 0 < b < 1.
19. Tutorial--Exponential Functions in Tabular and Graph Form: Example 17. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: 0 < a < 1, b = -1.
20. Tutorial--Exponential Functions in Tabular and Graph Form: Example 18. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: a = -1, 0 < b < 1.
21. Tutorial--Exponential Functions in Tabular and Graph Form: Example 19. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a = 1, b = 1.
22. Tutorial--Exponential Functions in Tabular and Graph Form: Example 20. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a > 1, b = 1.
23. Tutorial--Exponential Functions in Tabular and Graph Form: Example 21. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a = 1, b > 1.
24. Tutorial--Exponential Functions in Tabular and Graph Form: Example 22. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a > 1, b > 1.
25. Tutorial--Exponential Functions in Tabular and Graph Form: Example 23. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a = -1, b = -1.
26. Tutorial--Exponential Functions in Tabular and Graph Form: Example 24. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a < -1, b = -1.
27. Tutorial--Exponential Functions in Tabular and Graph Form: Example 25. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a = -1, b < -1.
28. Tutorial--Exponential Functions in Tabular and Graph Form: Example 26. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a < -1, b < -1.
29. Tutorial--Exponential Functions in Tabular and Graph Form: Example 27. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: -1 < a < 0, b = 1.
30. Tutorial--Exponential Functions in Tabular and Graph Form: Example 28. In this
tutorial, construct a function table and graph for an exponential function of base
10 of the form y = a*10^(bx) with these characteristics: a = 1, -1 < b < 0.
31. Tutorial--Quadratic Functions in Tabular and Graph Form: Example 29. In
this tutorial, construct a function table and graph for a quadratic function in
standard form with these characteristics: a < -1, b < -1, c = -1.
32. Tutorial--Exponential Functions in Tabular and Graph Form: Example 30. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: -1 < a < 0, b = -1.
33. Tutorial--Exponential Functions in Tabular and Graph Form: Example 31. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: a = -1, -1 < b < 0.
34. Tutorial--Exponential Functions in Tabular and Graph Form: Example 32. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: 0 < a < 1, b = 1.
35. Tutorial--Exponential Functions in Tabular and Graph Form: Example 33. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: a = 1, 0 < b < 1.
36. Tutorial--Exponential Functions in Tabular and Graph Form: Example 34. In this
tutorial, construct a function table and graph for an exponential function of base
10 of the form y = a*10^(bx) with these characteristics: 0 < a < 1, 0 < b < 1.
37. Tutorial--Exponential Functions in Tabular and Graph Form: Example 35. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: 0 < a < 1, b = -1.
38. Tutorial--Exponential Functions in Tabular and Graph Form: Example 36. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: a = -1, 0 < b < 1.
39. Tutorial--Exponential Functions in Tabular and Graph Form: Example 37. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: a = 1, b = 1.
40. Tutorial--Exponential Functions in Tabular and Graph Form: Example 38. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a > 1, b = 1.
41. Tutorial--Exponential Functions in Tabular and Graph Form: Example 39. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a = 1, b > 1.
42. Tutorial--Exponential Functions in Tabular and Graph Form: Example 40. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a > 1, b > 1.
43. Tutorial--Exponential Functions in Tabular and Graph Form: Example 41. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a = -1, b = -1.
44. Tutorial--Exponential Functions in Tabular and Graph Form: Example 42. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a < -1, b = -1.
45. Tutorial--Exponential Functions in Tabular and Graph Form: Example 43. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a = -1, b < -1.
46. Tutorial--Exponential Functions in Tabular and Graph Form: Example 44. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a < -1, b < -1.
47. Tutorial--Exponential Functions in Tabular and Graph Form: Example 45. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: -1 < a < 0, b = 1.
48. Tutorial--Exponential Functions in Tabular and Graph Form: Example 46. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: a = 1, -1 < b < 0.
49. Tutorial--Exponential Functions in Tabular and Graph Form: Example 47. In this
tutorial, construct a function table and graph for an exponential function of base
e of the form y = a*e^(bx) with these characteristics: -1 < a < 0, -1 < b < 0.
50. Tutorial--Exponential Functions in Tabular and Graph Form: Example 48. In this
tutorial, construct a function table and graph for an exponential function of base
e of the form y = a*e^(bx) with these characteristics: -1 < a < 0, b = -1.
51. Tutorial--Exponential Functions in Tabular and Graph Form: Example 49. In this
tutorial, construct a function table and graph for an exponential function of base
e of the form y = a*e^(bx) with these characteristics: a = -1, -1 < b < 0.
52. Tutorial--Exponential Functions in Tabular and Graph Form: Example 50. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: 0 < a < 1, b = 1.
53. Tutorial--Exponential Functions in Tabular and Graph Form: Example 51. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a = 1, 0 < b < 1.
54. Tutorial--Exponential Functions in Tabular and Graph Form: Example 52. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: 0 < a < 1, 0 < b < 1.
55. Tutorial--Exponential Functions in Tabular and Graph Form: Example 53. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: 0 < a < 1, b = -1.
56. Tutorial--Exponential Functions in Tabular and Graph Form: Example 54. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: a = -1, 0 < b < 1.