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

6. 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.

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

8. Draw a mapping for g(f(x)) -2 0 1 2 3 4 5 -3 1 3 5 7 9 11 36 4 36 100 196 324 484

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

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

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

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

13. 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

14. Find and graph the formulas for and

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

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