Warm Up Evaluate each expression for a = 2, b = –3, and c = 8. 1. a + 3 c

1. 1 2 c + b Warm Up Evaluate each expression for a = 2, b = –3, and c = 8. 1. a + 3c 2.ab – c 3. 26 –14 1 4. 4c – b 35 5. ba + c 17

2. Objectives Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values.

3. Vocabulary independent variable dependent variable function rule function notation

4. The inputof a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.

5. Directions: Identify the independent and dependent variables in the situation.

6. Example 1 A painter must measure a room before deciding how much paint to buy. The amount of paintdependson the measurement of a room. Dependent: amount of paint Independent: measurement of the room

7. Example 2 The height of a candle decrease d centimeters for every hour it burns. The height of a candledepends on the number of hours it burns. Dependent: height of candle Independent: time

8. Example 3 A veterinarian must weight an animal before determining the amount of medication. The amount of medicationdepends on the weight of an animal. Dependent: amount of medication Independent: weight of animal

9. Helpful Hint There are several different ways to describe the variables of a function. Independent Variable Dependent Variable y-values x-values Domain Range Input Output x f(x)

10. Example 4 A company charges $10 per hour to rent a jackhammer. The cost to rent a jackhammerdependson the length of time it is rented. Dependent variable: cost Independent variable: time

11. Example 5 Camryn buys p pounds of apples at $0.99 per pound. The cost of applesdepends on the number of pounds bought. Dependent variable: cost Independent variable: pounds

12. input x 2 You can think of a function as an input-output machine. 6 function f(x)=5x 5x 10 30 output

13. Directions: Evaluate the function for the given input values.

14. Example 6 For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4. f(x) = 3(x) + 2 f(x) = 3(x) + 2 Substitute 7 for x. Substitute –4 for x. f(–4) = 3(–4) + 2 f(7) = 3(7) + 2 Simplify. = –12 + 2 = 21 + 2 Simplify. = 23 = –10

15. Example 7 For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2. g(t) = 1.5t– 5 g(t) = 1.5t– 5 g(6) = 1.5(6) – 5 g(–2) = 1.5(–2) – 5 = –3– 5 = 9– 5 = 4 = –8

16. For , find h(r) when r = 600 and when r = –12. Example 8 = 202 = –2

17. Example 9 For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3. h(c) = 2c– 1 h(c) = 2c– 1 h(1) = 2(1) – 1 h(–3) = 2(–3) – 1 = 2– 1 = –6– 1 = 1 = –7

18. Example 10 For g(t) = , find g(t) when t = –24 and when t = 400. = –5 = 101

19. Lesson Summary: Part I Identify the independent and dependent variables. 1. A buffet charges $8.95 per person. independent: number of people dependent: cost 2. A moving company charges $130 for weekly truck rental plus $1.50 per mile. independent: miles dependent: cost

20. Lesson Summary: Part II Evaluate each function for the given input values. 3. For g(t) = , find g(t) when t = 20 and when t = –12. g(20) = 2 g(–12) = –6 4. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5. f(3.5) = 20 f(–5) = –31