1. Evaluation of Functions

2. Objective: * evaluates a function.

3. Evaluating Functions Example: f(x) = Example: f(x) = 3x - 2 if x = -2 f(x) = f(x) = 3x - 2 f(-2) = f(-2) = 3(-2) – 2 what if x = 7 ? f(-2) = f(-2) = -6-2 f(-2) = f(-2) = -8

4. Evaluating Functions Example: f(x) = Example: f(x) = 2x 2 + 5x - 49 f(4) = f(4) = 2(4) 2 + 5(4) - 49 what if x = 4 ? f(4) = 32+20 f(4) = 32+20 -49 f(4) = f(4) = 3 f(x) = f(x) = 2x 2 + 5x - 49 f(4) = f(4) = 2(16) + 20 - 49

5. Evaluating Functions f(-4) = f(-4) = 14 f(3) = 17

6. Evaluating Functions Target number of Shirt Sales5009001300 Price per T-Shirt The price function(x) =640-0.2(x) represents the price for which you can sell x printed T-shirts. What must be the price of the shirt for the first 2 entries in the table

7. Evaluating Functions: If f(x) = If f(x) = x + 8, evaluate each f(4), f(-9), f(-x), f(x +3) a. f(4), b. f(-9), c. f(-x), d. f(x +3) If f(x) = If f(x) = x 2 - 4x + 5,evaluate each f(3) f(-2), f(x + 1) a. f(3) b. f(-2), c. f(x + 1)

8. Evaluating Functions: If f(x) = If f(x) = x 2 - 4x + 5,evaluate each f(3) f(-2), f(x + 1) a. f(3) b. f(-2), c. f(x + 1) At Joe's pizzeria a pizza costs $5 with the first topping, and then an additional 75 cents for each additional topping. If x represents the number of toppings on a pizza, what function represents the cost of pizza with at least one topping?

9. Operation of Functions

10. Objectives: * performs addition, subtraction, multiplication, division, and composition of functions *solves problems involving functions.

11. SUM OF FUNCTIONS Let f(x) = 2 ; 3 Let f(x) = 3x 2 - 4x + 5 ; g(x) = 2x 3 + 6x - 2 Find (f + g)(x) = f(x) + Find (f + g)(x) = f(x) + g(x) (f + g)(x) = f(x) + (f + g)(x) = f(x) + g(x) 2 + 3 = 3x 2 - 4x + 5 + 2x 3 + 6x – 2 32 = 2x 3 + 3x 2 + 2x + 3 Operation of Functions

12. DIFFERENCE OF FUNCTIONS Operation of Functions

13. DIFFERENCE OF FUNCTIONS

14. Operation of Functions DIFFERENCE OF FUNCTIONS

15. Operation of Functions PRODUCT OF FUNCTIONS

16. Operation of Functions QUOTIENT OF FUNCTIONS

17. COMPOSITE FUNCTIONS Operation of Functions

18. COMPOSITE FUNCTIONS Operation of Functions Find (h ∘ g)(x) (h ∘ g)(x) = x + 1

19. COMPOSITE FUNCTIONS Operation of Functions Find [f ∘ (g + h) ](x)

20. Operation of Functions