©
Y
t
2
j
0
G
1
i
2
c
N
K
f
u
g
t
g
a
a
a
S
o
o
j
f
E
t
H
w
L
a
f
r
f
e
Y
4
L
B
L
6
C
q
.
O
d
7
A
9
l
R
l
m
s
r
p
i
r
g
h
h
z
t
N
s
N
b
r
o
e
V
s
C
e
6
r
2
v
Z
e
r
d
T
.
R
5
D
M
u
a
O
d
S
e
H
G
w
s
i
E
t
6
h
K
A
I
R
n
n
f
8
i
R
n
H
i
u
t
P
e
k
I
A
b
l
6
g
k
e
E
b
c
r
R
a
t
P
2
u
.
j
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Graphing Simple Rational Functions
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each.
1)
f
(
x
)
=
−
4
x
2)
f
(
x
)
=
4
x − 1
+ 1
3)
f
(
x
)
=
−
3
x − 1
− 1 4)
f
(
x
)
=
−
3
x
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. Then sketch the
graph.
5)
f
(
x
)
=
3
x + 1
− 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
6)
f
(
x
)
=
3
x + 1
+ 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
-1-
©
e
V
2
c
0
Q
1
i
2
A
M
K
P
u
Q
t
G
a
L
Y
S
P
o
d
f
B
t
j
w
P
a
E
r
e
e
f
Q
L
H
L
i
C
D
.
a
N
l
A
4
l
W
l
i
O
r
J
i
S
g
2
h
9
t
s
s
x
9
r
g
e
O
s
u
e
T
r
t
v
9
e
E
d
l
.
M
U
o
M
H
a
o
d
C
e
3
B
w
b
i
a
t
S
h
G
s
I
J
n
B
f
A
i
2
n
x
i
O
t
A
e
a
j
A
3
l
J
g
m
e
E
b
A
r
p
a
N
0
2
3
.
s
Worksheet by Kuta Software LLC
7)
f
(
x
)
=
3
x
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
8)
f
(
x
)
=
2
x − 3
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
9)
f
(
x
)
=
−
4
x + 1
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
10)
f
(
x
)
=
4
x
+ 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Critical thinking question:
11) Write a function of the form
f (
x) =
a
x −
h
+
k with a vertical asymptote at
x = 25
-2-
©
m
a
2
Y
0
c
1
F
2
r
w
K
l
u
c
t
O
a
j
P
S
V
o
N
f
e
t
s
w
u
a
k
r
m
e
x
Y
L
r
L
Z
C
0
.
3
w
E
A
K
l
r
l
b
8
r
S
i
2
g
v
h
V
t
L
s
g
H
r
r
e
s
s
s
e
m
r
e
v
9
e
D
d
D
.
h
J
g
M
k
a
m
d
a
e
L
g
w
5
i
h
t
4
h
O
8
I
d
n
z
f
n
i
D
n
X
i
R
t
4
e
t
l
A
V
l
O
g
F
e
u
b
l
r
N
a
d
o
2
2
.
7
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Graphing Simple Rational Functions
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each.
1)
f
(
x
)
=
−
4
x
Vertical Asym.:
x = 0
Horz. Asym.:
y = 0
Domain: All reals except 0
Range: All reals except 0
2)
f
(
x
)
=
4
x − 1
+ 1
Vertical Asym.:
x = 1
Horz. Asym.:
y = 1
Domain: All reals except 1
Range: All reals except 1
3)
f
(
x
)
=
−
3
x − 1
− 1
Vertical Asym.:
x = 1
Horz. Asym.:
y = −1
Domain: All reals except 1
Range: All reals except −1
4)
f
(
x
)
=
−
3
x
Vertical Asym.:
x = 0
Horz. Asym.:
y = 0
Domain: All reals except 0
Range: All reals except 0
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. Then sketch the
graph.
5)
f
(
x
)
=
3
x + 1
− 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertical Asym.:
x = −1
Horz. Asym.:
y = −2
Domain:
All reals except −1
Range:
All reals except −2
6)
f
(
x
)
=
3
x + 1
+ 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertical Asym.:
x = −1
Horz. Asym.:
y = 2
Domain:
All reals except −1
Range:
All reals except 2
-1-
©
O
Q
2
h
0
6
1
r
2
D
j
K
d
u
M
t
s
a
q
9
S
R
o
u
f
l
t
B
w
s
a
G
r
y
e
a
c
L
g
L
p
C
F
.
G
7
Y
A
j
l
j
l
C
3
r
y
i
x
g
L
h
9
t
N
s
b
m
r
R
e
D
s
8
e
X
r
V
v
k
e
x
d
Z
.
r
p
D
M
3
a
G
d
T
e
D
B
w
W
i
4
t
D
h
5
M
I
l
n
q
f
J
i
a
n
c
i
j
t
A
e
N
N
A
Z
l
a
g
c
e
R
b
Q
r
j
a
y
P
2
L
.
z
Worksheet by Kuta Software LLC
7)
f
(
x
)
=
3
x
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertical Asym.:
x = 0
Horz. Asym.:
y = 1
Domain:
All reals except 0
Range:
All reals except 1
8)
f
(
x
)
=
2
x − 3
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertical Asym.:
x = 3
Horz. Asym.:
y = 1
Domain:
All reals except 3
Range:
All reals except 1
9)
f
(
x
)
=
−
4
x + 1
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertical Asym.:
x = −1
Horz. Asym.:
y = 1
Domain:
All reals except −1
Range:
All reals except 1
10)
f
(
x
)
=
4
x
+ 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertical Asym.:
x = 0
Horz. Asym.:
y = 2
Domain:
All reals except 0
Range:
All reals except 2
Critical thinking question:
11) Write a function of the form
f (
x) =
a
x −
h
+
k with a vertical asymptote at
x = 25
Many answers. Ex:
f (
x) =
1
x − 25
-2-
Create your own worksheets like this one with
Infinite Algebra 2
. Free trial available at KutaSoftware.com