Tutorials: Linear Functions in Tabular and Graph Form

This document discusses various types of linear transformations, including rotations, reflections, shears, dilations, projections, and their representations as matrices. It provides examples of transforming lines and triangles under rotations of different angles. Linear transformations are important in computer graphics for modifying objects by changing their position, size, orientation or shape. Matrix representations allow linear transformations to be described geometrically.

Geometrical transformation

This document discusses different types of geometric transformations including translations, reflections, rotations, and dilations. It provides examples and notations for each type of transformation. Translations involve sliding an object along a vector, reflections involve flipping an object across a line, rotations involve turning an object around a fixed point, and dilations involve changing the size of an object. The document also discusses isometric transformations, lines of reflection, and applications of transformations including tessellations. Examples are provided to demonstrate different transformations and how to find equations of lines of reflection.

Slope of a line

Rhea Rose Almoguez

The document discusses slope and how to calculate it. It defines slope as the steepness of a line or the rate of change between two points. Slope is represented by the letter m. There are three main ways to calculate slope: 1) using the formula m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2); 2) by finding the rise over run when given a graph; 3) by taking the coefficient of x when a line equation is in the form of y = mx + b, where m represents the slope. Examples are provided to demonstrate calculating slope using these different methods.

2001 transformations reflections etc

This document provides instructions for completing a geometry drill on identifying transformations and graphing transformations in the coordinate plane. It includes examples of identifying reflections, rotations, translations from preimage to image. It also includes examples of writing rules for translations between figures in the coordinate plane and applications to art history. The objectives are to identify reflections, rotations, translations, and graph transformations in the coordinate plane.

Functions

wilde1kd

A function is a machine that takes an input X and produces a single output Y. Functions can be displayed as tables by plugging in X values and listing the corresponding Y values. Functions can also be displayed as graphs by plotting the X and Y values and connecting the points. The domain is the set of all possible X values, while the range is the set of all possible Y values. A relation is only a function if each X value corresponds to a single Y value. The zeros of a function are the X values where the function equals 0. Functions can be combined, transformed, and have their slope and y-intercept calculated according to standard mathematical operations.

Empfohlen

Functions intro

Ron Eick

Algebra 1 power pointlr

tlrumer

Slope

maranaluca

Matrix of linear transformation 1.9-dfs

Geometrical transformation

Slope of a line

Rhea Rose Almoguez

2001 transformations reflections etc

Functions

wilde1kd

3functions

Andrea Domenech

This document contains 7 exercises for a functions test in 3rd year secondary education (ESO). The exercises cover: drawing graphs that do and do not represent functions; analyzing graphs of functions including domain, range, continuity, and extrema; sketching graphs that meet given criteria for domain, intercepts, and extrema; determining equations of lines given points and slopes; finding the slope and y-intercept of a given line; sketching the graph of a polynomial function; and sketching the graph of a piecewise defined function.

Presentation 2

CarleeHopkins

1) Slope-intercept form is an equation of a line that includes the slope and y-intercept. 2) There are different ways to write a line equation in slope-intercept form depending on what information is given: the slope and y-intercept, a graph of the line, or two points on the line. 3) If given two points on a line, you can find the slope and then use point-slope form to write the equation, which can then be converted to slope-intercept form.

Tutorials--Graphing Linear Functions in Slope-Intercept Form

Notes on 3.2 properties of linear frunction graphs

joannahstevens

The document discusses key properties of linear function graphs, including that the y-intercept is the y-value when x=0 and the x-intercept is the x-value when y=0. It defines slope as m in the slope-intercept equation y=mx+b and describes horizontal and vertical lines having slopes of 0 and undefined respectively. It lists three common forms for linear functions: slope-intercept, point-slope, and Ax+By=C and provides examples of transforming between the forms.

2001 transformations reflections etc

This document provides examples and explanations of different types of geometric transformations, including reflections, rotations, translations, and combinations. Key points: - Transformations change the position, size, or shape of a figure. The original is the preimage and result is the image. - Translations can be described by rules that specify adding or subtracting values from the x- and y-coordinates. - Examples show identifying transformations from diagrams and writing rules for translations between figures. - A quiz provides practice applying concepts to new examples involving reflections, rotations and translations.

January 8

khyps13

Hermit curves & beizer curves

KKARUNKARTHIK

This document discusses Hermite curves and Bezier curves. Hermite curves are defined by two endpoints and the tangent vectors at those endpoints. This provides enough information to define a cubic Hermite spline. Bezier curves use control points and Bernstein polynomials to define the curve. Both curves use parametric equations and have properties like following the shape of control points and containing curves within the convex hull of control points. The document also discusses B-spline curves, which provide automatic continuity, and NURBS curves, which extend B-splines to be rational curves using weights.

Functions

Siyavula

The document defines and explains different types of functions including linear, quadratic, hyperbolic, exponential, sine, cosine, and tangent functions. It describes how each type of function is represented through equations, tables, graphs and ordered pairs. Key aspects like domains, ranges, periods, asymptotes and effects of variables on the shape of graphs are discussed for each function type.

B spline surfeces

ramac123

B-spline surfaces are constructed using a grid of control points and blending functions. The blending functions are polynomials defined over intervals in each parametric direction. This allows a B-spline surface to be defined by blending between control points. Properties include continuity and local influence of control points. A surface can be subdivided by inserting knots or raising the degree. Rational B-spline surfaces use homogeneous coordinates to represent common surfaces like planes and spheres. NURBS are the basis for CAD standards like IGES.

Slope Nov 17

DMCI

The document defines slope as the steepness and direction of a line, calculated as the rise over the run or change in y over the change in x between two points on the line. It provides examples of calculating the slope between two points and finding the y-value of a third point given the slope. It also describes how the sign of the slope indicates whether a line is diagonal up/right, horizontal, or diagonal down/right and when the slope is undefined when the line is vertical.

Sub notes 1

Nov 17 Slope

DMCI

The document defines slope as the steepness and direction of a line, calculated as the rise over the run or change in y over the change in x between two points on the line. It provides examples of calculating the slope between two points and finding the y-value of a third point given the slope. It also describes how the sign of the slope indicates whether a line is diagonal left, horizontal, or diagonal right and whether the slope is undefined if the line is vertical.

Day 9 examples u6f13

Exponential functions have exponents that cause the output y to increase as the input x increases from left to right. Functions with a fractional base between 0 and 1 are decreasing, while those with a base greater than 1 are increasing. Exponential functions are defined for all real numbers as inputs and have outputs greater than 0, with the horizontal axis y=0 as an asymptote. Their graphs can be derived from the base graph y=2x and transformed through multiplication or division of the base.

New day 8 examples

ST ZULAIHA NURHAJARURAHMAH

Exponential functions involve exponents where the input variable is the exponent. As the input variable increases from left to right on the graph, the output variable also increases, making exponential functions increasing functions. Exponential functions have characteristics such as having a domain of all real numbers, a range greater than 0, and a horizontal asymptote of y=0. Whether an exponential function is increasing or decreasing depends on if the base is greater than 1 or between 0 and 1.

Gradient of graph

Mohd Muzlimi Junoh

Function transformations

Terry Gastauer

The document discusses function transformations including translations, reflections, dilations, and compressions. It defines these transformations and provides examples of how they affect the graph of a function. Translations slide the graph left or right without changing its shape or orientation. Reflections create a mirror image of the graph across an axis, flipping it. Compressions squeeze the graph towards or away from an axis. Dilations stretch or shrink the graph away from an axis. The document explains how to interpret various function notation and applies the transformations to example graphs.

Solving systems of linear equations by graphing lecture

Kaiya Duppins

This document discusses solving systems of linear equations by graphing. It defines a system of linear equations as two or more equations containing at least one variable. It explains that to solve a system by graphing, each equation should be written in slope-intercept form and then graphed on the same set of axes. The type of solution can be determined by examining the graphs - one solution if the lines intersect, no solution if the lines are parallel, or infinitely many solutions if the lines coincide. It provides examples to illustrate each type of solution and explains that the point of intersection or coinciding point(s) will be the solution(s) to plug back into the original system to check.

Solution of linear system of equations

The document summarizes techniques for solving linear systems of equations. It discusses direct solution methods like Gaussian elimination that transform the system into an upper triangular system and then use back substitution to solve. Gaussian elimination involves using elementary row operations to eliminate values below the diagonal of the coefficient matrix. The document also discusses concepts like consistency, uniqueness of solutions, and ill-conditioned systems. It provides examples of applying elementary row operations during the Gaussian elimination process.

Chapter 3. linear equation and linear equalities in one variables

monomath

Polynomials And Linear Equation of Two Variables

Ankur Patel

linear equation

kanishkaanandkv

1) The document discusses linear equations in two variables, including defining their form as ax + by = c, explaining that they have infinitely many solutions, and noting that their graphs are straight lines. 2) Specific topics covered include finding solutions, drawing graphs, identifying equations for lines parallel to the x-axis and y-axis, and providing examples of writing and solving linear equations. 3) The summary restates the key points about the properties of linear equations in two variables, such as their graphical and algebraic representations.

Factoring Perfect Square Trinomial

Dhenz Lorenzo

The document discusses factoring perfect square trinomials (polynomials with three terms where the first and last terms are perfect squares). It provides examples of factoring expressions like x^2 + 8x + 16 into (x + 4)^2. For an expression to be a perfect square trinomial, the first term must be a perfect square, the third term must be a perfect square, and the middle term must be twice the product of the square roots of the first and last terms. Students are provided examples and exercises to practice factoring various square trinomial expressions.

Weitere ähnliche Inhalte

Was ist angesagt?

3functions

Andrea Domenech

Presentation 2

CarleeHopkins

Tutorials--Graphing Linear Functions in Slope-Intercept Form

Notes on 3.2 properties of linear frunction graphs

joannahstevens

2001 transformations reflections etc

January 8

khyps13

Hermit curves & beizer curves

Functions

B spline surfeces

Slope Nov 17

Sub notes 1

Nov 17 Slope

The document defines slope as the steepness and direction of a line, calculated as the rise over the run or change in y over the change in x between two points on the line. It provides examples of calculating the slope between two points and finding the y-value of a third point given the slope. It also describes how the sign of the slope indicates whether a line is diagonal left, horizontal, or diagonal right and whether the slope is undefined if the line is vertical.

Day 9 examples u6f13

New day 8 examples

ST ZULAIHA NURHAJARURAHMAH

Gradient of graph

Mohd Muzlimi Junoh

Function transformations

Terry Gastauer

Was ist angesagt? (16)

3functions

Presentation 2

Tutorials--Graphing Linear Functions in Slope-Intercept Form

Notes on 3.2 properties of linear frunction graphs

2001 transformations reflections etc

January 8

Hermit curves & beizer curves

Functions

B spline surfeces

Slope Nov 17

Sub notes 1

Nov 17 Slope

Day 9 examples u6f13

New day 8 examples

Gradient of graph

Function transformations

Andere mochten auch

Solving systems of linear equations by graphing lecture

Kaiya Duppins

Solution of linear system of equations

Chapter 3. linear equation and linear equalities in one variables

monomath

Polynomials And Linear Equation of Two Variables

Ankur Patel

linear equation

kanishkaanandkv

Factoring Perfect Square Trinomial

Dhenz Lorenzo

Andere mochten auch (6)

Solving systems of linear equations by graphing lecture

Solution of linear system of equations

Chapter 3. linear equation and linear equalities in one variables

Polynomials And Linear Equation of Two Variables

linear equation

Factoring Perfect Square Trinomial

Ähnlich wie Tutorials: Linear Functions in Tabular and Graph Form

Tutorials--Quadratic Functions in Tabular and Graphic Form

Tutorials--Function Inverses

Tutorials--Functions and Their Inverses

Tutorials--Sine Functions in Tabular and Graph Form

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--Absolute Value Functions in Tabular and Graph Form

Tutorials--Tangent Functions in Tabular and Graph Form

Tutorials--Logarithmic Functions in Tabular and Graph Form

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).

Linear_and_NonLinear_Functions_a (1).pptx

AhmedMohamedMohamedE

This document provides an overview of linear and non-linear functions for an 8th grade math class. It defines linear functions as those that form a straight line when graphed, while non-linear functions do not. Linear functions can be represented by graphs, equations in slope-intercept form (y=mx+b), or tables with constant rates of change for both x- and y-values. Non-linear functions have curved graphs or tables without constant rates of change. Examples of linear and non-linear equations and tables are provided to illustrate the differences.

Tutorials--Square Root Functions in Tabular and Graph Form

Ähnlich wie Tutorials: Linear Functions in Tabular and Graph Form (9)

Tutorials--Quadratic Functions in Tabular and Graphic Form

Tutorials--Function Inverses

Tutorials--Functions and Their Inverses

Tutorials--Sine Functions in Tabular and Graph Form

Tutorials--Absolute Value Functions in Tabular and Graph Form

Tutorials--Tangent Functions in Tabular and Graph Form

Tutorials--Logarithmic Functions in Tabular and Graph Form

Linear_and_NonLinear_Functions_a (1).pptx

Tutorials--Square Root Functions in Tabular and Graph Form

Mehr von Media4math

Geometric Construction: Creating a Teardrop Shape

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.

Pumpkin π: A Multi-Grade Math Activity

Math in the News: Issue 112--Back-to-School Purchases

Math in the News: Issue 111--Summer Blockbusters

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.

Math in the News Issue 110: Summer Travel

Media4Math Overview

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...

Tutorials--The Language of Math--Variable Expressions--Multiplication and Add...

Tutorials--The Language of Math--Numerical Expressions--Grouping Symbols

Tutorials--The Language of Math--Numerical Expressions--Multiplication

Tutorials--The Language of Math--Numerical Expressions--Division

Tutorials--The Language of Math--Numerical Expressions--Subtraction

Tutorials--Language of Math--Numerical Expressions--Addition

Math in the News: Issue 107

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--Cube Root Functions in Tabular and Graph Form

Tutorials--Secant Functions in Tabular and Graph Form

Tutorials--Cosecant Functions in Tabular and Graph Form

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--Cosine Functions in Tabular and Graph Form

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--Rational Functions in Tabular and Graph Form

Tutorials--Exponential Functions in Tabular and Graph Form