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MATHEMATICAL MODELING
Scientists, Engineers, and Economist have
always used mathematics to model the
real world.
A mathema...
PAID AND UNPAID WORKERS
ECONOMIC GROWTH
INDUSTRIAL GROWTH
MATHEMATICAL MODELING
Numerical Model
Algebraic Models
Graphical Models
FUNDAMENTALS
VOCABULARY
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 th...
APPLICATION
FUNCTION DEFINITION AND NOTATION
Function
f(x)
INPUT
OUTPUT
WAYS TO REPRESENT A FUNCTION
x2
x1
x3
x4
x2
x1
x3
y2
y1
y3
y2
y1
y3
Mapping
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 intersec...
DOMAIN AND RANGE
To find the domain we look for all the x-
coordinates that correspond to points on
the graph.
To find the...
FINDING THE DOMAIN OF A FUNCTION
Algebraically or graphically
Careful when a variable is in the denominator, the
denominat...
HOMEWORK
Page 75 #11 - 17 all, 21
Page 95 #9 – 23 odd
Section 1.1
Section 1.1
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Section 1.1

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Transcript of "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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