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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Graphing Logarithms
Identify the domain and range of each. Then sketch the graph.
1)
y =
log
6
(
x − 1
)
− 5
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
2)
y =
log
5
(
x − 1
)
+ 3
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
3)
y =
log
6
(
x − 3
)
− 5
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
4)
y =
log
2
(
x − 1
)
+ 3
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
5)
y =
log
4
(
x + 1
)
− 4
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
6)
y =
log
5
(
x + 1
)
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
-1-
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Worksheet by Kuta Software LLC
7)
y =
log
4
(
x + 2
)
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
8)
y =
log
6
(
x − 2
)
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
9)
y =
log
4
(
3
x + 11
)
− 5
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
10)
y =
log
5
(
2
x + 2
)
+ 5
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
11)
y =
log
6
(
3
x + 14
)
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
12)
y =
log
2
(
4
x − 11
)
− 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Graphing Logarithms
Identify the domain and range of each. Then sketch the graph.
1)
y =
log
6
(
x − 1
)
− 5
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x > 1
Range: All reals
2)
y =
log
5
(
x − 1
)
+ 3
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x > 1
Range: All reals
3)
y =
log
6
(
x − 3
)
− 5
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x > 3
Range: All reals
4)
y =
log
2
(
x − 1
)
+ 3
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x > 1
Range: All reals
5)
y =
log
4
(
x + 1
)
− 4
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x > −1
Range: All reals
6)
y =
log
5
(
x + 1
)
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x > −1
Range: All reals
-1-
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Worksheet by Kuta Software LLC
7)
y =
log
4
(
x + 2
)
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x > −2
Range: All reals
8)
y =
log
6
(
x − 2
)
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x > 2
Range: All reals
9)
y =
log
4
(
3
x + 11
)
− 5
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x >
−
11
3
Range: All reals
10)
y =
log
5
(
2
x + 2
)
+ 5
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x > −1
Range: All reals
11)
y =
log
6
(
3
x + 14
)
+ 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x >
−
14
3
Range: All reals
12)
y =
log
2
(
4
x − 11
)
− 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Domain:
x >
11
4
Range: All reals
-2-
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