# Graphing Rational Functions WITH ANSWERS

```
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











 x












 x


 x

8) f ( x) =
x  x
 x  x

y










x
 x





7) f ( x) =
y



 x













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-1-
y
Worksheet by Kuta Software LLC

 x   x
9) f ( x) = 
x  x




x   x
10) f ( x) =
 x   x
y











 x






12) f ( x) =
y










 x











y









 x












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-2-

 x



 x



 x

x



y


14) f ( x) =

x
 x





 x   x
13) f ( x) =
x   x







x   x
11) f ( x) =
 x


y
y
Worksheet by Kuta Software LLC


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.

 x  x
x
Discontinuities: , 
2) f ( x) =
Discontinuities: 
x
Vertical Asym.: x, x
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
1) f ( x) =

Holes: None
Horz. Asym.: None
X-intercepts: , , 
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
6) f ( x) =


y
Discontinuities: , 
Vertical Asym.: x, x
Holes: None
Horz. Asym.: y




x
 x







 x









8) f ( x) =
y
x  x
 x  x

y
Discontinuities: , 
Vertical Asym.: x
Holes: x
Horz. Asym.: None




 x

Discontinuities: 
Vertical Asym.: x
Holes: None

Horz. Asym.: y









x
 x





7) f ( x) =
Discontinuities: 
Vertical Asym.: x
Holes: None

Horz. Asym.: y




y




 x













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-1-


 x
Worksheet by Kuta Software LLC


 x   x
9) f ( x) = 
x  x

x   x
10) f ( x) =
 x   x
y
Discontinuities: , 
Vertical Asym.: x, x
Holes: None
Horz. Asym.: y











 x






12) f ( x) =
y
Discontinuities: 
Vertical Asym.: x
Holes: None
Horz. Asym.: None



 x









14) f ( x) =






 x
y
Discontinuities: 
Vertical Asym.: x
Holes: None
Horz. Asym.: y





x
Discontinuities: , 
Vertical Asym.: x
Holes: x
Horz. Asym.: y

Discontinuities: 
Vertical Asym.: x
Holes: None

Horz. Asym.: y




 x
y


y









x
 x


Discontinuities: , 
Vertical Asym.: x, x
Holes: None
Horz. Asym.: None






 x   x
13) f ( x) =
x   x








y


x   x
11) f ( x) =
 x


 x















 x
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
```