1. Warm-Up

2. 7.6 Function Operations

3. With your table, try to extend what you know about adding and subtracting two functions and apply your knowledge to the following problem. How might we solve this?
If f(x) = 2x2 + 3x + 10 and g(x) = 3x – 2, then evaluate (f × g)(2).

4. Review: What is a function?
A relationship where every domain (x value has exactly one unique range (y value).
Sometimes we talk about a FUNCTION MACHINE, where a rule is applied to each input of x

5. Function Operations

6. Adding and Subtracting Functions

7. Multiplying Functions

8. Dividing Functions

9. Let’s Try Some

10. Let’s Try Some

11. Let’s Try Some

12. Let’s Try Some

13. Function Composition Notation This does not say “FOG”
You read this “f composed with g of x”

14. Function Composition
Notation
Another way to write this is
OR f[g(x)]

15. Function Composition
Notation

16. Function Composition EX 1: f(x) = x2 g(x) = x + 1OR
EX 1: f(x) = x2 g(x) = x + 1
Start with g(x) and put that in to f(x)
= (x + 1)2
= x2 + 2x + 1

17. Function Composition EX 2: f(x) = x + 2 g(x) = 4 – x2
Start with g(x) and put that in to f(x)
= (4 – x2) + 2
= -x2 + 6

18. Function Composition EX 3: f(x) = x2 + 1 g(x) = 2x
Start with g(x) and put that in to f(x)
= (2x)2 + 1
= 4x2 + 1

19. evaluating with Function Composition (Numbers)
EX 4: f(x) = x g(x) = 2x
Start with g(x) & find g(3). Put that answer in to f(x).
g(3) = 6
f(6) = 37

20. Exit Ticket