Graphing Rational Functions

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Kuta Software - Infinite Algebra 2
Name___________________________________
Graphing Rational Functions
Date________________
Period____
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
6)
f ( x) =
x
x
y
y
x
x
7)
f ( x) =
x
x
8)
f ( x) =
x x
x x
y
y
x
x

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x x
x x
9) f ( x) =
10) f ( x) =
x x
x x
y
y
x
x
11)
f ( x) =
x x
x
12)
f ( x) =
x
x
y
y
x
x
13)
f ( x) =
x x
x x
14)
f ( x) =
x
y
y
x
x

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Kuta Software - Infinite Algebra 2
Graphing Rational Functions
Name___________________________________
Date________________
Period____
Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of
each.
x
1) f ( x) =
Discontinuities: , 2) f ( x) =
x x
Vertical Asym.: x, x
x
Discontinuities:
Vertical Asym.: x
Holes: None
Holes: None
Horz. Asym.: y
Horz. Asym.: y
X-intercepts: None
X-intercepts:
x x x
x x
3) f ( x) =
Discontinuities: , 4) f ( x) =
Discontinuities: ,
x x
Vertical Asym.: x, x
x x
Vertical Asym.: x
Holes: None
Holes: x
Horz. Asym.: None
X-intercepts: , ,
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
6)
f ( x) =
x
x
y
Discontinuities: ,
Vertical Asym.: x, x
Holes: None
Horz. Asym.: y
y
Discontinuities:
Vertical Asym.: x
Holes: None
Horz. Asym.: y
x
x
7)
f ( x) =
x
x
8)
f ( x) =
x x
x x
y
Discontinuities:
Vertical Asym.: x
Holes: None
Horz. Asym.: y
y
Discontinuities: ,
Vertical Asym.: x
Holes: x
Horz. Asym.: None
x
x

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9)
x x
f ( x) =
x x
y
Discontinuities: ,
Vertical Asym.: x, x
Holes: None
Horz. Asym.: y
10)
x x
f ( x) =
x x
y
Discontinuities: ,
Vertical Asym.: x, x
Holes: None
Horz. Asym.: None
x
x
11)
f ( x) =
x x
x
12)
f ( x) =
x
x
y
Discontinuities:
Vertical Asym.: x
Holes: None
Horz. Asym.: None
y
Discontinuities:
Vertical Asym.: x
Holes: None
Horz. Asym.: y
x
x
13)
f ( x) =
x x
x x
14)
f ( x) =
x
y
Discontinuities: ,
Vertical Asym.: x
Holes: x
Horz. Asym.: y
y
Discontinuities:
Vertical Asym.: x
Holes: None
Horz. Asym.: y
x
x
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