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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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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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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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
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Worksheet by Kuta Software LLC
