graphing simple rational functions
DESCRIPTION
Math Rational FunctionTRANSCRIPT
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Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________Graphing Simple Rational FunctionsIdentify the vertical asymptotes, horizontal asymptote, domain, and range of each.
1)
f (
x) =
4
x2)
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 thegraph.
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-
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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
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Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________Graphing Simple Rational FunctionsIdentify the vertical asymptotes, horizontal asymptote, domain, and range of each.
1)
f (
x) =
4
x
Vertical Asym.:
x = 0Horz. Asym.:
y = 0Domain: All reals except 0Range: All reals except 0
2)
f (
x) =
4
x 1 + 1
Vertical Asym.:
x = 1Horz. Asym.:
y = 1Domain: All reals except 1Range: All reals except 1
3)
f (
x) =
3
x 1 1
Vertical Asym.:
x = 1Horz. Asym.:
y = 1Domain: All reals except 1Range: All reals except 1
4)
f (
x) =
3
x
Vertical Asym.:
x = 0Horz. Asym.:
y = 0Domain: All reals except 0Range: All reals except 0
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. Then sketch thegraph.
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 = 1Horz. Asym.:
y = 2Domain: All reals except 1Range: 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 = 1Horz. Asym.:
y = 2Domain: All reals except 1Range: All reals except 2
-1-
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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 = 0Horz. Asym.:
y = 1Domain: All reals except 0Range: 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 = 3Horz. Asym.:
y = 1Domain: All reals except 3Range: 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 = 1Horz. Asym.:
y = 1Domain: All reals except 1Range: 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 = 0Horz. Asym.:
y = 2Domain: All reals except 0Range: 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
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