1. Warm Up Evaluate each expression for a = 2, b = –3, and c = 8.
2. ab – c 3. 26
–14 1 2
c + b 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 input of a function is the independent variable
The input of 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 paint depends on 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 candle depends 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 medication depends 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
x-values
y-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 jackhammer depends on 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 apples depends on the number of pounds bought.
Dependent variable: cost
Independent variable: pounds

12. You can think of a function as an input-output machine.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(7) = 3(7) + 2
f(–4) = 3(–4) + 2 =
Simplify.
Simplify.
= –12 + 2
= 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
= 9 – 5
= –3 – 5
= 4
= –8

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