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

2. Check It Out! Example 1
Determine a relationship between the x- and y-values. Write an equation.
{(1, 3), (2, 6), (3, 9), (4, 12)} x 1 2 3 4 y 3 6 9 12
Step 1 List possible relationships between the first x- or y-values.
1  3 = 3 or = 3

3. 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.

4. Example 2A: Identifying Independent and Dependent Variables
Identify the independent and dependent variables
in the situation.
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

5. Example 2B: Identifying Independent and Dependent Variables
Identify the independent and dependent variables
in the situation.
The height of a candle decreases 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

6. Example 2C: Identifying Independent and Dependent Variables
Identify the independent and dependent variables
in the situation.
A veterinarian must weigh 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

7. 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)

8. Check It Out! Example 2a
Identify the independent and dependent variable in the situation.
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

9. Check It Out! Example 2b
Identify the independent and dependent variable in the situation.
Apples cost $0.99 per pound.
The cost of apples depends on the number of pounds bought.
Dependent variable: cost
Independent variable: pounds

10. Example 3A: Writing Functions
Identify the independent and dependent variables. Write an equation in function notation for the situation.
A math tutor charges $35 per hour.
The fee a math tutor charges depends on number of hours.
Dependent: fee
Independent: hours
Let h represent the number of hours of tutoring.
The function for the amount a math tutor charges is f(h) = 35h.

11. Example 3B: Writing Functions
Identify the independent and dependent variables. Write an equation in function notation for the situation.
A fitness center charges a $100 initiation fee plus $40 per month.
The total cost depends on the number of months, plus $100.
Dependent: total cost
Independent: number of months
Let m represent the number of months
The function for the amount the fitness center charges is f(m) = 40m

12. Check It Out! Example 3a
Identify the independent and dependent variables. Write an equation in function notation for the situation.
Steven buys lettuce that costs $1.69/lb.
The total cost depends on how many pounds of lettuce Steven buys.
Dependent: total cost
Independent: pounds
Let x represent the number of pounds Steven buys.
The function for the total cost of the lettuce is f(x) = 1.69x.

13. Check It Out! Example 3b
Identify the independent and dependent variables. Write an equation in function notation for the situation.
An amusement park charges a $6.00 parking fee plus $29.99 per person.
The total cost depends on the number of persons in the car, plus $6.
Dependent: total cost
Independent: number of persons in the car
Let x represent the number of persons in the car.
The function for the total park cost is
f(x) = 29.99x + 6.

14. You can think of a function as an input-output machine
You can think of a function as an input-output machine. For Tasha’s earnings, f(x) = 5x. If you input a value x, the output is 5x.
input x 2 6
function
f(x)=5x 5x 10 30
output

15. Example 4A: Evaluating Functions
Evaluate the function for the given input values.
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

16. Example 4B: Evaluating Functions
Evaluate the function for the given input values.
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

17. Example 4C: Evaluating Functions
Evaluate the function for the given input values.
For , find h(r) when r = 600 and when r = –12.
= 202
= –2

18. Check It Out! Example 4a
Evaluate the function for the given input values.
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

19. Check It Out! Example 4b
Evaluate the function for the given input values.
For g(t) = , find g(t) when t = –24 and when t = 400.
= –5
= 101

20. Lesson Quiz: Part I
Identify the independent and dependent variables. Write an equation in function notation for each situation.
1. A buffet charges $8.95 per person.
independent: number of people
dependent: cost
f(p) = 8.95p
2. A moving company charges $130 for weekly truck rental plus $1.50 per mile.
independent: miles
dependent: cost
f(m) = m

21. Lesson Quiz: 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

22. Lesson Quiz: Part III
Write a function to describe the situation. Find the reasonable domain and range for the function.
5. A theater can be rented for exactly 2, 3, or 4 hours. The cost is a $100 deposit plus $200 per hour.
f(h) = 200h + 100
Domain: {2, 3, 4}
Range: {$500, $700, $900}