

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
1) f ( x) = 
2) f ( x) =
 x  x x

x   x   x x   x

3) f ( 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.

 x
5) f ( x) =  
6) f ( x) =
x  x  x
y y
 

 

 

 

        x         x
 

 

 

 

x x  x
7) f ( x) = 8) f ( x) = 
 x  x  x
y y
 

 

 

 

        x         x
 

 

 

 

©3 M2H011n2G tKfu7tUaM jSZoafStgwza4rGe8 4L9LWCo.o w mAblXlS 5rMi4gQhUthsa VrReas3e2revreBdU.a P BMBahdAeH iw2iJtLhf lI9nJfciZnXiVtJeX qABlRgme4bXrsaM k2K.w -1- Worksheet by Kuta Software LLC


 x   x x   x
9) f ( x) =  10) f ( x) =
x  x  x   x
y y
 

 

 

 

        x         x
 

 

 

 

x   x x
11) f ( x) = 12) f ( x) =
 x  x
y y
 

 

 

 

        x         x
 

 

 

 

 x   x 
13) f ( x) = 14) f ( x) =
x   x x
y y
 

 

 

 

        x         x
 

 

 

 

©n E2O0B1b2T 4Kyu7tlaO US9o5fVtvwyaXrneb 3LWLhCL.N 7 VAWlhlB erMiNgzhktXsr VrheRsYemrJv1eHdJ.z t jMRakd7ea zwJiftwhY gIOnifzidnOiDtUel zAplegMeXburoaT J2f.u -2- 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
1) f ( x) = Discontinuities: , 

2) f ( x) = Discontinuities: 
 x  x
Vertical Asym.: x, 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
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.

 x
5) f ( x) =  
6) f ( x) =
x  x  x
y y
 Discontinuities: ,   Discontinuities: 
Vertical Asym.: x, x Vertical Asym.: x
 Holes: None  Holes: None
Horz. Asym.: y 
Horz. Asym.: y
  

 

        x         x
 

 

 

 

x x  x
7) f ( x) = 8) f ( x) = 
 x  x  x
y y
 Discontinuities:   Discontinuities: , 
Vertical Asym.: x Vertical Asym.: x
 Holes: None  Holes: x
 Horz. Asym.: None
Horz. Asym.: y
  

 

        x         x
 

 

 

 

©0 E2i0E1S2v xKJultdam GSOovfItKwJa2reeR hLXLLC4.p W tA0lelK jrvitgRh2tOs9 mrEeZsoeUrGvLead0.H n MMLaRdce6 awliptphJ jIbnlfmiCn4i8tje7 NA3lkgOeFb4rWan e2Z.q -1- Worksheet by Kuta Software LLC



 x   x x   x
9) f ( x) =  10) f ( x) =
x  x  x   x
y y
 Discontinuities: ,   Discontinuities: , 
Vertical Asym.: x, x Vertical Asym.: x, x
 Holes: None  Holes: None
Horz. Asym.: y Horz. Asym.: None
 

 

        x         x
 

 

 

 

x   x x
11) f ( x) = 12) f ( x) =
 x  x
y y
 Discontinuities:   Discontinuities: 
Vertical Asym.: x Vertical Asym.: x
 Holes: None  Holes: None
Horz. Asym.: None 
Horz. Asym.: y
  

 

        x         x
 

 

 

 

 x   x 
13) f ( x) = 14) f ( x) =
x   x x
y y
 Discontinuities: ,   Discontinuities: 
Vertical Asym.: x Vertical Asym.: x
 Holes: x  Holes: None
Horz. Asym.: y Horz. Asym.: y
 

 

        x         x
 

 

 

 

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com

©6 m2F0y1T23 wKoujtUan zSVonfxtqwfaJrwex DLuL1Cz.x N XAclQlu 5rRi5gmh8tRsC urielsAesrTvweHdv.E U rMJazdke9 dwFiotCh6 wIVnufriYnzi8tGei WAUlDgmekbmr6aO 022.W -2- Worksheet by Kuta Software LLC