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Section 1.1

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Section 1.1

1. 1. 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.
2. 2. PAID AND UNPAID WORKERS
3. 3. ECONOMIC GROWTH
4. 4. INDUSTRIAL GROWTH
5. 5. MATHEMATICAL MODELING Numerical Model Algebraic Models Graphical Models
6. 6. FUNDAMENTALS
7. 7. VOCABULARY
8. 8. 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
9. 9. APPLICATION
10. 10. FUNCTION DEFINITION AND NOTATION Function f(x) INPUT OUTPUT
11. 11. WAYS TO REPRESENT A FUNCTION x2 x1 x3 x4 x2 x1 x3 y2 y1 y3 y2 y1 y3 Mapping
12. 12. 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.
13. 13. 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.
14. 14. 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.
15. 15. HOMEWORK Page 75 #11 - 17 all, 21 Page 95 #9 – 23 odd
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