Graphing Rational Functions.ks-ia2, Lecture notes of Algebra

Worksheet by Kuta Software LLC. Kuta Software - Infinite Algebra 2 ... Graphing Rational Functions. Identify the points of discontinuity, holes, ...

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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-
pf3
pf4

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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.

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

 f (  x ) =  x   x 

 f (  x ) =  x    x    x    x ^   x 

 f (  x ) =  x    x     x ^   x  Identify the points of discontinuity, holes, vertical asymptotes, and horizontal asymptote of each. Then sketch the graph.

 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

©n E 2 O0B 1b2T 4 Kyu7t l aO US 9 o5fVt vwyaXrne b 3 LW LhC L .N 7 VAW l hl B e rMi Ngzhkt Xs r Vrhe R s YemrJ v1eHdJ.z t j M R akd7e a zwJi f t whY gIOni fzi dnOi Dt Ue l z Apl egMeXbur oaT J 2f.u Worksheet by Kuta Software LLC

f (

x ) =  

x ^ 

x  x



x 

x

y

f (

x ) =  x ^ 

x  

x



x 

x

y

f (

x ) =  x



x  

x 

x

y

f (

x ) =  x   

x 

x

y

f (

x ) =  

x ^ 

x   x ^ 

x 

x

y

f (

x ) =   x 

x

y

-2-

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f (

x ) =  

x ^ 

x  x



x 

x

y

       

        Discontinuities:^ ,^  Vertical Asym.:

x ,

x 

Holes: None Horz. Asym.:

y 

f (

x ) =  x ^ 

x  

x



x 

x

y

       

        Discontinuities:^ ,^  Vertical Asym.:

x ,

x 

Holes: None Horz. Asym.: None

f (

x ) =  x



x  

x 

x

y

       

        Discontinuities:^  Vertical Asym.:

x 

Holes: None Horz. Asym.: None

f (

x ) =  x   

x 

x

y

       

        Discontinuities:^  Vertical Asym.:

x 

Holes: None Horz. Asym.:

y  

f (

x ) =  

x ^ 

x   x ^ 

x 

x

y

       

        Discontinuities:^ ,^  Vertical Asym.:

x 

Holes:

x 

Horz. Asym.:

y 

f (

x ) =   x 

x

y

       

        Discontinuities:^  Vertical Asym.:

x 

Holes: None Horz. Asym.:

y 

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