Name ——————————————————————
Date ———————————
SPI 0806.3.7
Identify, compare and contrast functions as linear or nonlinear.
The vertical line test is used to determine whether a relation represented by a graph is a function.
A relation is a function provided that no vertical line passes through more than one point on the graph.
Function
Not a Function
y
y
1
22
O
2
O
x
1
x
22
The graph of a linear function must pass the vertical line test and it must be a straight line with no
bends.
Linear Function
Nonlinear Function
y
y
1
1
21
© Houghton Mifflin Harcourt Publishing Company
1
21
x
Which statement about linear and
nonlinear functions is always true?
2
A The graph of a nonlinear function
B
The graph of a linear function has a
negative slope.
C
The graph of a nonlinear function is
parallel to the x-axis.
D The graph of a linear function is a
line.
Which equation represents a linear
function?
F
has a positive slope.
x
3x 5 y
G y 5 x2
3
H
y 5 2x3
J
2x4 5 y 1 5
Which equation represents a linear
function?
A x3 1 2 5 y
B
x
y 1 __
2 5 21
C
y 5 2x2
D y 5 x4 1 3
GO ON
Grade 8 Tennessee
8_MTNBETP478555_SPI_0806.3.7.indd 63
SPI 0806
63
8/28/10 4:51:31 PM
Name ——————————————————————
SPI 0806.3.7
4
(continued)
Each of these graphs is the graph of a
linear function, except which one?
F
4
5
Which graph is the graph of a function?
A
y
2
0
-4
Date ———————————
x
-2
2
4
-2
B
-4
y
G
2
0
-4
C
x
-2
2
4
-2
-4
4
y
D
2
0
-4
x
-2
2
4
-2
-4
6
J
4
y
F
2
0
-4
-2
x
2
-2
-4
Which statement about functions and
linear functions is true?
The graph of a function may have an
undefined slope.
G The graph of a linear function may
have an undefined slope.
4
H
The graph of a linear function may
be parallel to the x-axis.
J
The graph of a linear function may
be parallel to the y-axis.
© Houghton Mifflin Harcourt Publishing Company
H
GO ON
64
SPI 0806
8_MTNBETP478555_SPI_0806.3.7.indd 64
Grade 8 Tennessee
8/28/10 4:51:32 PM
Name ——————————————————————
SPI 0806.3.7
7
Date ———————————
(continued)
Each table of values represents points on
the graphs of four different lines.
9
Which graph is the graph of a linear
function?
A
y
x
y
x
y
0
0
0
0
3
1
3
2
3
2
1
2
6
4
6
3
9
6
9
x
y
x
y
0
0
0
5
3
3
3
7
6
6
6
9
9
9
9
11
4
24 23 22 21 0
21
22
23
1 2 3
4 x
1 2 3
4 x
1 2 3
4 x
1 2 3
4 x
24
B
y
4
3
2
1
Which statement about the graphs of the
lines is true?
24 23 22 21 0
21
22
23
A None of the lines represent linear
functions.
24
B
One line represents a linear function.
C
Three lines represent linear
functions.
C
y
4
3
© Houghton Mifflin Harcourt Publishing Company
D All of the lines represent linear
2
1
functions.
8
24 23 22 21 0
21
22
23
Which lines represent the graph of a
function?
24
\
4
3
D
y
4
p
3
1
24 23 22
2
22
23
1
2
3 4 [
r
q
F
lines q and r
s
H lines q, r, and s
G lines s and p and s J
2
1
24 23 22 21 0
21
22
23
24
lines p, q, r,
GO ON
Grade 8 Tennessee
8_MTNBETP478555_SPI_0806.3.7.indd 65
SPI 0806
65
8/28/10 4:51:33 PM
Name ——————————————————————
SPI 0806.3.7
10
(continued)
This chart shows the unit cost per item for
quantities in multiples of 1,000.
11
In this graph of a linear function, what
relationship appears to be shared by the
n- and p-coordinates of points on the line?
Quantity
Unit Cost
1,000
$0.15
8
2,000
$0.14
3,000
$0.13
6
4
2
4,000
$0.12
5,000
$0.10
Is the relationship shared by the data an
example of a linear function? Why or why
not?
F
Date ———————————
No, because graphing the data
requires axes that are not labeled
x and y.
p
28 26 24 22
22
2 4
6
8 n
24
26
28
A The value of p is 1 less than twice
the value of n.
B
The value of n is 1 less than twice
the value of p.
not a straight line.
C
The value of p is one-half the value
of n.
H
Yes, because any multiple of 1,000
can be purchased at a fixed unit cost.
D The value of n is greater than the
J
Yes, because the data can be
graphed.
value of p.
© Houghton Mifflin Harcourt Publishing Company
G No, because the graph of the data is
GO ON
66
SPI 0806
8_MTNBETP478555_SPI_0806.3.7.indd 66
Grade 8 Tennessee
8/28/10 4:51:34 PM