Graphing Simple Rational Functions - Kuta Software

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Kuta Software - Infinite Algebra 2
Name___________________________________
Graphing Simple Rational Functions
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each.
Date________________ Period____
1) f (x) = − 4 x
2) f (x) =
4
x − 1 + 1
3) f (x) = − 3
x − 1 − 1
4) f (x) = − 3 x
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. Then sketch the
graph.
5) f (x) =
3
x + 1 − 2
6) f (x) =
3
x + 1 + 2
8
y
8
y
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
−2
x
−8 −6 −4 −2 2 4 6 8
−2
x
−4
−4
−6
−6
−8
−8

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8
7) f (x) = 3 x + 1 x
8) f (x) =
2
x − 3 + 1
y
8
y
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
9) f (x) = − 4
x + 1 + 1
8
y
8
10) f (x) = 4 x + 2 x
y
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
Critical thinking question:
11) Write a function of the form f (x) =
a
x − h
+ k with a vertical asymptote at x = 25

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Kuta Software - Infinite Algebra 2
Name___________________________________
Graphing Simple Rational Functions
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each.
Date________________ Period____
1) f (x) = − 4 x
Vertical Asym.: x = 0
Horz. Asym.: y = 0
Domain: All reals except 0
Range: All reals except 0
2) f (x) =
4
x − 1 + 1
Vertical Asym.: x = 1
Horz. Asym.: y = 1
Domain: All reals except 1
Range: All reals except 1
3) f (x) = − 3
x − 1 − 1
Vertical Asym.: x = 1
Horz. Asym.: y = −1
Domain: All reals except 1
Range: All reals except −1
4) f (x) = − 3 x
Vertical Asym.: x = 0
Horz. Asym.: y = 0
Domain: All reals except 0
Range: All reals except 0
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. Then sketch the
graph.
5) f (x) =
3
x + 1 − 2
y
8 Vertical Asym.: x = −1
Horz. Asym.: y = −2
6
Domain:
All reals except −1
4
Range:
All reals except −2
2
6) f (x) =
3
x + 1 + 2
y
8 Vertical Asym.: x = −1
Horz. Asym.: y = 2
6
Domain:
All reals except −1
4
Range:
All reals except 2
2
−8 −6 −4 −2 2 4 6 8
−2
x
−8 −6 −4 −2 2 4 6 8
−2
x
−4
−4
−6
−6
−8
−8

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7) f (x) = 3 x + 1 x
y
8 Vertical Asym.: x = 0
Horz. Asym.: y = 1
6
Domain:
All reals except 0
4
Range:
All reals except 1
2
8) f (x) =
2
x − 3 + 1
y
8 Vertical Asym.: x = 3
Horz. Asym.: y = 1
6
Domain:
All reals except 3
4
Range:
All reals except 1
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
9) f (x) = − 4
x + 1 + 1
10) f (x) = 4 x + 2 x
y
8 Vertical Asym.: x = −1
Horz. Asym.: y = 1
6
Domain:
All reals except −1
4
Range:
All reals except 1
2
y
8 Vertical Asym.: x = 0
Horz. Asym.: y = 2
6
Domain:
All reals except 0
4
Range:
All reals except 2
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
Critical thinking question:
11) Write a function of the form f (x) =
1
Many answers. Ex: f (x) =
x − 25
a
x − h
+ k with a vertical asymptote at x = 25
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