2. MATHEMATICAL MODELING
Scientists, Engineers, and Economist have
always used mathematics to model the
real world.
A mathematical model is a mathematical
structure that approximates phenomena
for the purpose of studying or predicting
their behavior.

3. PAID AND UNPAID WORKERS

4. ECONOMIC GROWTH

5. INDUSTRIAL GROWTH

6. MATHEMATICAL MODELING
Numerical Model
Algebraic Models
Graphical Models

7. FUNDAMENTALS

8. VOCABULARY

9. APPLICATION
A bakery sells a 9” by 13” cake for the
same price as an 8” diameter round
cake. If the round cake is twice the
height of the rectangular cake, which
option gives the most cake for the
money?
Rectangular cake

10. APPLICATION

12. FUNCTION DEFINITION AND NOTATION
Function
f(x)
INPUT
OUTPUT

13. WAYS TO REPRESENT A FUNCTION
x2
x1
x3
x4
x2
x1
x3
y2
y1
y3
y2
y1
y3
Mapping

14. WAYS TO REPRESENT A FUNCTION
A graph in the xy-plane defines y as a function of
x if and only if no vertical line intersects the graph
in more than one point.

15. DOMAIN AND RANGE
To find the domain we look for all the x-
coordinates that correspond to points on
the graph.
To find the range we look for all the y-
coordinates that correspond to points on
the graph.

16. FINDING THE DOMAIN OF A FUNCTION
Algebraically or graphically
Careful when a variable is in the denominator, the
denominator can not equal zero.
Careful when a variable is under an even radical
sign, radicand mut be greater than or equal to zero.
When graphing, be careful with hidden behavior.

17. HOMEWORK
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