Compositions Notes Add earlier graphs where they have to say what is f(3)… 1/16/2019.

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Domain: 1) f(0) = 8 2) f(3) = 3) g(-2) = -2 4) g(2) = 0 5) f(g(0)) = f(2) =0 6) f(g(-2)) = f(-2) =undefined 7) f(g(2)) = f(0) =8 8) f(g(-1)) = f(1) =3.

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Presentation transcript:

Compositions Notes Add earlier graphs where they have to say what is f(3)… 1/16/2019

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 Area Function: Book Domain: (0,4) … Alternative 1/16/2019

Homework page 64 #88 B. Book Range: (32,64) Alternative (0,64) Sometimes there are multiple interpretations of an authentic problem. Problems can have multiple solutions 1/16/2019

Homework page 64 #88 C. If the figure has no area If x=4, the figure is a square with side 1/16/2019

Agenda Combining Functions Function Compositions 1/16/2019

Function Algebra 1/16/2019

Example Given find such that: a. a: b. b: c. c: 1/16/2019

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)) 1/16/2019

Examples If and then 1/16/2019

Graphical Example Based on the function to right, what is 1/16/2019

Example If and then 1/16/2019

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)). 1/16/2019

Reflection Is for all functions, f and g? Counterexample: No, this is not true…composition is not commutative, order matters. Counterexample: 1/16/2019

Fractal Curves are made via a function composition process Show & Tell Fractal Curves are made via a function composition process 1/16/2019

Composition Calisthenics F G F o G Match across the columns 1/16/2019

Homework Pg 89 #6-12(even) Pg 90 #44-50 (even) Pg 91 #62 1/16/2019