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Compositions Notes

Compositions Notes. Add earlier graphs where they have to say what is f(3)…. Function Compositions. Lecture: 2D Pre AP & GT Precalculus. Homework page 64 #88. Corners of equal size are cut from a square with sides of length 8 meters A. Write the area of the figure as a function of

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Compositions Notes

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  1. Compositions Notes • Add earlier graphs where they have to say what is f(3)…

  2. Function Compositions Lecture: 2DPre AP & GT Precalculus

  3. Homework page 64 #88 • Corners of equal size are cut from a square with sides of length 8 meters • A. Write the area of the figure as a function of • Area Function: • Book Domain: (0,4) … Alternative

  4. Homework page 64 #88 B. Book Range: (32,64) Alternative (0,64) Sometimes there are multiple interpretations of anauthentic problem. Problems can have multiple solutions

  5. Homework page 64 #88 If x=4, the figure is a square with side C. If the figure has no area

  6. Agenda • Combining Functions • Function Compositions

  7. Function Algebra

  8. Example • Given find such that: • a. • a: • b. • b: • c. • c:

  9. Composition • We say, “f composed with g of x” OR “f of g of x” • Range of g(x) is the domain of f(g(x))

  10. Examples • If and then

  11. Graphical Example Based on the function to right, what is

  12. Example • If and then

  13. Composition Graphically • The point a is in the domain The red line is the range of f(x)but is also the domain of g(f(x)) On a graph to change from domain to range shift left to y=x to find corresponding domain element of g(x) Then find corresponding point in the range of g(x) and hence the range of g(f(x)).

  14. Reflection • Is for all functions, f and g? • No, this is not true…composition is not commutative, order matters. Counterexample:

  15. Show & Tell Fractal Curves are made via a function composition process

  16. Composition Calisthenics Match across the columns

  17. Homework • Pg 89 #6-12(even)Pg 90 #44-50 (even) • Pg 91 #62

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