Page 1 of 5
Graphing Functions
BEFORE
Now
WHY?
You graphed ordered pairs
in a coordinate plane.
You’ll graph functions in a
coordinate plane.
So you can write a function for the
cost of papayas, as in Ex. 15.
In the Real World
Fabric You are in a craft shop, choosing
fabric for a sewing project. The fabric
you choose costs $2.50 for each yard.
How can you use a graph to represent
this situation? You’ll find the answer
in Example 2.
Word Watch
linear function, p. 355
You can graph a function by creating
an input-output table, forming ordered
pairs, and plotting the ordered pairs.
EXAMPLE
1
Graphing a Function
Graph the function y 2x 1.
with
Solving
When the domain of a
function is not given,
assume that it includes
every x-value for which the
function can produce a
corresponding y-value.
1 Make an input-output table by
choosing several input values
and evaluating the output values.
2 Use the table to write a list of
ordered pairs:
(2, 3), (1, 1), (0, 1),
(1, 3), (2, 5)
x
2
1
0
1
2
Substitution
y 2(2) 1
y 2(1) 1
y 2(0) 1
y 2(1) 1
y 2(2) 1
3 Plot the ordered pairs in a
coordinate plane.
4 Notice that all of the points lie on
a line. Any other ordered pairs
satisfying y 2x 1 would also
lie on the line when graphed. The
line represents the complete
graph of the function y 2x 1.
Your turn now
354
Chapter 7
y
5
4
3
2
1
3 2
y 2x 1
1
2
3
Graph the function.
1. y x 3
Equations, Inequalities, and Functions
2. y 3x
y
3
1
1
3
5
3. y 2x 3
2
3
4 x
Page 2 of 5
EXAMPLE
tch Out!
Wa
In Example 2,
note that you cannot have
less than 0 yards of fabric,
so you cannot use any
numbers less than 0 in
the domain.
2
Writing and Graphing a Function
The situation described on page 354 can be represented by the function
y 2.50x, where y is the total cost of the fabric and x is the number of
yards of fabric.
Follow these steps to graph the function.
1 Make an input-output
table.
Input x
0
1
2
3
4
2 Plot the ordered pairs and
connect them as shown.
y
Output y
0
2.5
5
7.5
10
10
8
6
4
2
2
y 2.50x
2
4
6
8 10 12 x
Linear Functions The functions in Examples 1 and 2 are linear functions.
A linear function is a function whose graph is a line or part of a line.
Not all graphs are lines, nor do all graphs represent functions.
EXAMPLE
with
Solving
Recall that a function
pairs each input value
with exactly one output
value.
3
Identifying Linear Functions
Tell whether each graph represents a function of x. If it does,
tell whether the function is linear or nonlinear.
a.
b.
y
3
2
1
3 2
O
2
(1, 1)
1
2 x
c.
y
3
y
3
2
O
1
5
4
3
2
2 x
(1, 1)
2
O
1
2
3 x
Solution
a. This graph represents a function of x. The function is linear because
the graph is a line.
b. This graph does not represent a function of x. For each value of x in
the domain, excluding 2, there is more than one value of y.
c. This graph represents a function of x. The function is nonlinear
because the graph is not a line.
Lesson 7.8
Graphing Functions
355
Page 3 of 5
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 711
Getting Ready to Practice
1. Vocabulary What is the difference between a linear function and
a nonlinear function?
Match the function with its graph.
1
3. y x
2
B.
2. y 3x
A.
y
5
4
3
O
C.
y
y
3
2
1
3
2
1
3 2
1
3
4. y 2x 3
1
1
2
2 x
1
2
3 x
2
2 x
5. Walking When you walk slowly, your body burns about 2 Calories
every minute. This situation can be represented by the function y 2x,
where y is the number of calories burned and x is the number of
minutes you walk. Graph the function.
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
6–14
15–16, 18–21
22–24, 28
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Graph the function.
6. y x
9. y x 3
1
12. y x 2
4
1
8. y x
3
7. y 10 x
10. y 3x 5
11. y 4x 1
13. y 0.5x 2
14. y x 4
15. Papayas Papayas cost $1.50 per pound. Write and graph a function
that models the cost y of x pounds of papayas.
1
16. Bicycles The front wheel of a bicycle travels 6 feet for every rotation
2
it makes. Write and graph a function that models the distance y the
front wheel travels in x rotations.
17. Writing Describe a situation that can be represented by a linear
function.
Write and graph a function that converts the units.
356
Chapter 7
18. x yards to y feet
19. x days to y weeks
20. x pints to y cups
21. x millimeters to y centimeters
Equations, Inequalities, and Functions
Page 4 of 5
Tell whether the graph represents a function of x. If it does, tell
whether the function is linear or nonlinear.
22.
23.
y
5
4
3
2
1
2
O
24.
y
y
3
2
1
3
2
1
2
1
2
1
2
O
3 x
2
3
4 x
2
2
3 x
1
In Exercises 25–27, write y as a function of x. Then graph the
function.
EXAMPLE
Writing y as a Function of x
8x 4y 1200
Original equation
8x 8x 4y 1200 8x
Subtract 8x from each side.
4y 1200 8x
Simplify.
4y
1200 8x
4
4
Divide each side by 4.
y 300 2x
Simplify.
ANSWER You can write 8x 4y 1200 as y 300 2x.
25. 3x y 2
26. 2x y 8
27. 15x 5y 30
28. Hot Chocolate The table below shows the temperature y of a cup of
hot chocolate after cooling for x minutes. Use the table to write a list of
ordered pairs. Plot the ordered pairs and draw a line or curve through
the points. Then tell whether the graph represents a function. If so, is it
a linear function?
Time (min)
0
2
5
10
20
30
Temperature (C)
90
85
79
68
58
49
40
50
43.5 39.5
60
37
Graph the functions in the same coordinate plane. Then tell where
they intersect.
29. y x and y 3x 4
30. y 5 x and y 2x 11
31. y x 3 and y 2x 8
32. y x 1 and y 3x 1
33. Challenge A rectangle has a length of 4 inches and a width of x inches.
Write and graph a function that gives the perimeter y of the rectangle.
Lesson 7.8
Graphing Functions
357
Page 5 of 5
Mixed Review
Write the fraction in simplest form. (Lesson 4.3)
77
35. 343
63
34. 81
120
36. 360
65
37. 78
38. Evaluate the function y 6x 7 when x 12. (Lesson 7.7)
Test-Taking Practice
39. Multiple Choice The graph of which
INTERNET
y
2
1
function is shown?
State Test Practice
CLASSZONE.COM
A. y x
B. y 6x
C. y x 6
D. y x 6
3 2
O
1
2
3 x
2
40. Multiple Choice Which ordered pair is a point on the graph of
the function y 2x 5?
F. (0, 0)
G. (5, 5)
H. (1, 2)
I. (3, 1)
Fun with Functions
Each player puts a marker on the START space. Players alternate turns.
On your turn, roll a number cube and evaluate the function using the
number rolled as the value of x. If the result is positive, move forward
that number of spaces. If the result is negative, move backward that
number of spaces. The first player to land on or pass the END space wins.
y= x+ 1
y = 2x
y = –x + 3
y = –2 x + 7
y= x– 5
y=
4
y = 2x – 4
y=–
2x +
y
= x+6
358
Chapter 7
y = –x + 1
y = –x – 1
y= x+ 4
y=x–1
y = 2x – 10
Equations, Inequalities, and Functions
y = –x + 5
y =–x – 3
–x
2
y=x+3
x+
ST AR T
y=x
y=
END