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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Graphing Rational Functions
Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of
each.
1)
f (
x) =
x
x
2)
f (
x) =
x
x
3)
f (
x) =
x
x
x
x
x
4)
f (
x) =
x
x
x
x
Identify the points of discontinuity, holes, vertical asymptotes, and horizontal asymptote of each. Then
sketch the graph.
5)
f (
x) =
x
x
x
y
6)
f (
x) =
x
x
x
y
7)
f (
x) =
x
x
x
y
8)
f (
x) =
x
x
x
x
x
y
-1-
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Worksheet by Kuta Software LLC
9)
f (
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x
x
x
x
x
y
10)
f (
x) =
x
x
x
x
x
y
11)
f (
x) =
x
x
x
x
y
12)
f (
x) =
x
x
x
y
13)
f (
x) =
x
x
x
x
x
y
14)
f (
x) =
x
x
y
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Graphing Rational Functions
Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of
each.
1)
f (
x) =
x
x
Discontinuities: ,
Vertical Asym.:
x,
x
Holes: None
Horz. Asym.:
y
X-intercepts: None
2)
f (
x) =
x
x
Discontinuities:
Vertical Asym.:
x
Holes: None
Horz. Asym.:
y
X-intercepts:
3)
f (
x) =
x
x
x
x
x
Discontinuities: ,
Vertical Asym.:
x,
x
Holes: None
Horz. Asym.: None
X-intercepts: , ,
4)
f (
x) =
x
x
x
x
Discontinuities: ,
Vertical Asym.:
x
Holes:
x
Horz. Asym.:
y
X-intercepts:
Identify the points of discontinuity, holes, vertical asymptotes, and horizontal asymptote of each. Then
sketch the graph.
5)
f (
x) =
x
x
x
y
Discontinuities: ,
Vertical Asym.:
x,
x
Holes: None
Horz. Asym.:
y
6)
f (
x) =
x
x
x
y
Discontinuities:
Vertical Asym.:
x
Holes: None
Horz. Asym.:
y
7)
f (
x) =
x
x
x
y
Discontinuities:
Vertical Asym.:
x
Holes: None
Horz. Asym.:
y
8)
f (
x) =
x
x
x
x
x
y
Discontinuities: ,
Vertical Asym.:
x
Holes:
x
Horz. Asym.: None
-1-
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Worksheet by Kuta Software LLC
9)
f (
x) =
x
x
x
x
x
y
Discontinuities: ,
Vertical Asym.:
x,
x
Holes: None
Horz. Asym.:
y
10)
f (
x) =
x
x
x
x
x
y
Discontinuities: ,
Vertical Asym.:
x,
x
Holes: None
Horz. Asym.: None
11)
f (
x) =
x
x
x
x
y
Discontinuities:
Vertical Asym.:
x
Holes: None
Horz. Asym.: None
12)
f (
x) =
x
x
x
y
Discontinuities:
Vertical Asym.:
x
Holes: None
Horz. Asym.:
y
13)
f (
x) =
x
x
x
x
x
y
Discontinuities: ,
Vertical Asym.:
x
Holes:
x
Horz. Asym.:
y
14)
f (
x) =
x
x
y
Discontinuities:
Vertical Asym.:
x
Holes: None
Horz. Asym.:
y
-2-
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