Chapter 3: Transformations of Graphs and Data Lesson 7: Compositions of Functions Mrs. Parziale.

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Chapter 3: Transformations of Graphs and Data Lesson 7: Compositions of Functions Mrs. Parziale

Composite Functions: The composite of two functions g with f is written g ◦ f or g( f(x)). The domain of g(f(x)) is the set of x-values in the domain of f for which f(x) is in the domain of g. – Simply put – the set of answers from f(x) become the input for the function g.

Example 1: Let and (a)Find f(g(3))(b) Find g(f(-2)) (start with g(3))

Draw a mapping for g(f(x))

Example 2: Let and (a)Find a rule for

Example 2: Let and (b) Find a rule for

Find the domain of the following: f ________________________ g ________________________ ____________________

Example 3: Let and Find f(g(4)) g(f(4))

Find and graph the formulas for and Since the rules do not produce the same results, we can conclude that composite functions are not commutative. f ◦ g  g ◦ f

Find and graph the formulas for and

Find the domain of the following: f ________________________ g ________________________ ____________________

Closure What is a composite function? How do you find ? Given the following: Find for x = 3