Page 1 of 4
Functions and Equations
Word Watch
function, p. 350
input, p. 350
output, p. 350
domain, p. 350
range, p. 350
BEFORE
Now
WHY?
You wrote and evaluated
expressions.
You’ll write and evaluate
function rules.
So you can find the pressure on a
scuba diver, as in Ex. 22.
A function is a pairing of each number in a
given set with exactly one number in another
set. Starting with a number called an input ,
the function associates it with exactly one
number called an output . A function can be
represented by a rule, a table, or a graph.
EXAMPLE
1
Input
Output
Evaluating a Function
Evaluate the function y 5x when x 7.
y 5x
Write rule for function.
5(7)
Substitute 7 for x.
35
Multiply.
Domain and Range The set of all input values is called the domain of a
function. The set of all output values is called the range of a function.
EXAMPLE
2
Making an Input-Output Table
Make an input-output table for the function y x 1.3 using the
domain 0, 1, 2, and 3. Then state the range of the function.
Solution
Input x
Substitution
0
1
2
3
y 0 1.3
y 1 1.3
y 2 1.3
y 3 1.3
1.3
0.3
0.7
1.7
Output y
The range of the function is the set of outputs: 1.3, 0.3, 0.7, and 1.7.
Your turn now
Complete the following exercise.
1. Make an input-output table for the function y 2x 2 using the
domain 2, 1, 0, 1, and 2. Then state the range of the function.
350
Chapter 7
Equations, Inequalities, and Functions
Page 2 of 4
EXAMPLE
3
Writing a Function Rule
Write a function rule for the input-output table.
Input x
2
1
0
1
2
3
4
Output y
0.5
1.5
2.5
3.5
4.5
5.5
6.5
Solution
You can see that you obtain each output by adding 2.5 to the input.
ANSWER The function rule given by the table is y x 2.5.
EXAMPLE
4
Writing a Function Rule From a Pattern
Cakes In the diagrams of the cakes, the input c is the number of cuts
made across the cake, and the output p is the number of pieces of cake.
Write a rule for the function. Then use the rule to find the number of
pieces made from 9 cuts.
Solution
1 Begin by making an
input-output table.
Input c
1
2
3
4
Output p
2
4
6
8
2 Notice that each output value is twice the input value. So, a rule
for the function is p 2c.
3 To find the number of pieces made from 9 cuts, evaluate the
function when c 9. Because p 2(9) 18, there are 18 pieces
made by 9 cuts.
Your turn now
2.
Write a function rule for the input-output table.
Input x
1
0
1
2
Output y
4
3
2
1
3.
Lesson 7.7
Input x
Output y
2
4
6
8
1
2
3
4
Functions and Equations
351
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 711
Getting Ready to Practice
1. Vocabulary In your own words, explain what a function is.
2. Copy and complete the input-output table for the function y 2x 5.
Input x
4
2
0
2
4
6
8
10
?
?
?
?
?
?
?
?
Output y
3. Find the Error Describe
and correct the error in
making an input-output
table for the function
y x 2.
Input x
2
1
0
1
0
1
2
3
Output y
4. Ages You are 3 years older than your cousin. Write a function rule
that represents your age y in terms of your cousin’s age x. Then create
an input-output table using the domain 10, 15, 20, and 25.
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
5–8
9–14, 22
15–18
20–21
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Evaluate the function y 3x 2 for the given value of x.
5. 4
6. 0
8. 3
7. 1
Make an input-output table for the function using the domain
–2, –1, 0, 1, and 2. Then state the range of the function.
9. y x 11
12. y x 4.56
10. y 20x
11. y 3.7x
13. y 0.8x 1
14. y 15 2x
Write a function rule for the input-output table.
15.
17.
Input x
1
2
3
4
Output y
5
10
15
20
Input x
Output y
16.
2
3
4
5
0.8
1.8
2.8
3.8
18.
Input x
2
1
0
1
Output y
13
14
15
16
Input x
3
0
3
6
1
0
1
2
Output y
19. Write a function rule that converts y years to m months. Use the
function to calculate the number of months in 20 years.
352
Chapter 7
Equations, Inequalities, and Functions
Page 4 of 4
Science
Write a function rule for the pattern. Each figure in the pattern is made
using unit squares. The input x is the number below each figure, and
the output y is the number of unit squares in the figure.
20.
21.
1
2
3
1
4
2
3
4
22. Scuba Diving The pressure on a scuba diver is given by the function
p 64d 2112, where p is pressure, in pounds per square foot, and d
is depth, in feet. Make an input-output table for depths of 0, 20, 40, 60,
80, and 100 feet. As the depth increases, what happens to the pressure?
Decide Tell whether the table represents a function. If so, write
the function rule. If not, explain why not.
23.
■
1
0
1
2
Output q
1
0
1
4
Input m
2
0
2
4
Output n
3
1
5
9
Scuba Diving
Input p
A scuba diver can reach
475 feet, relative to sea
level. The lowest point in the
ocean is 35,802 feet,
relative to sea level. What is
the difference between the
depth a scuba diver can
reach and the lowest point in
the ocean?
25.
24.
26.
Input s
1
1
4
4
Output t
1
1
2
2
Input a
3
1
1
3
Output b
13
3
7
17
27. Challenge Write three different functions for which an input of
3 gives an output of 15.
Mixed Review
28. Write the prime factorization of 84. (Lesson 4.1)
29. Solve 10z < 20. Then graph the solution. (Lesson 7.6)
Basic Skills Plot the points in a coordinate plane.
30. A(9, 2)
32. C(3, 4)
31. B(0, 2)
33. D(4, 0)
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
34. Multiple Choice Which function rule represents the table?
A. y x 2
B. y x
Input x
C. y x
D. y x 4
Output y
1
0
1
2
1
0
1
2
35. Multiple Choice What is the value of y 7x 2 when x 0.5?
F. 5.5
G. 4.5
H. 1.5
Lesson 7.7
I. 33
Functions and Equations
353