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Graphing Simple Rational Functions - Kuta Software
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Kuta Software - Infinite Algebra 2 ... Graphing Simple Rational Functions ... Worksheet by Kuta Software LLC. 7) f (x) = 3 x. + 1 x y. −8. −6. −4. −2. 2. 4. 6. 8. − 8. −6.
Kuta Software - Infinite Algebra 2
Name___________________________________
Graphing Simple Rational Functions
Date________________ Period____
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. 1) f ( x) = −
4 x
2) f ( x) =
3) f ( x) = −
3 −1 x−1
4) f ( x) = −
4 +1 x−1
3 x
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. Then sketch the graph. 5) f ( x) =
3 −2 x+1
6) f ( x) =
3 +2 x+1
y
−8
−6
−4
y
8
8
6
6
4
4
2
2
−2
2
4
6
8 x
−8
−6
−4
−2
2
−2
−2
−4
−4
−6
−6
−8
−8
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-1-
4
6
8 x
Worksheet by Kuta Software LLC
7) f ( x) =
3 +1 x
8) f ( x) =
2 +1 x−3
y
−8
−6
−4
9) f ( x) = −
y
8
8
6
6
4
4
2
2
−2
2
4
6
8 x
−8
−6
−4
−2
−2
−2
−4
−4
−6
−6
−8
−8
4 +1 x+1
10) f ( x) =
−6
−4
6
8 x
2
4
6
8 x
y
8
8
6
6
4
4
2
2
−2
4
4 +2 x
y
−8
2
2
4
6
8 x
−8
−6
−4
−2
−2
−2
−4
−4
−6
−6
−8
−8
Critical thinking question: 11) Write a function of the form f ( x) =
a + k with a vertical asymptote at x = 25 x−h
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Graphing Simple Rational Functions
Date________________ Period____
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. 1) f ( x) = −
4 x
2) f ( x) =
Vertical Asym.: x = 0 Horz. Asym.: y = 0 Domain: All reals except 0 Range: All reals except 0
3) f ( x) = −
4 +1 x−1
Vertical Asym.: x = 1 Horz. Asym.: y = 1 Domain: All reals except 1 Range: All reals except 1
3 −1 x−1
4) f ( x) = −
Vertical Asym.: x = 1 Horz. Asym.: y = −1 Domain: All reals except 1 Range: All reals except −1
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 −2 x+1
6) f ( x) =
y
3 +2 x+1 y
Vertical Asym.: x = −1 Horz. Asym.: y = −2 Domain: All reals except −1 Range: All reals except −2
8 6 4
6 4
2 −8
−6
−4
−2
Vertical Asym.: x = −1 Horz. Asym.: y = 2 Domain: All reals except −1 Range: All reals except 2
8
2 2
4
6
8 x
−8
−6
−4
−2
2
−2
−2
−4
−4
−6
−6
−8
−8
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-1-
4
6
8 x
Worksheet by Kuta Software LLC
7) f ( x) =
3 +1 x
8) f ( x) = y
2 +1 x−3 y
Vertical Asym.: x = 0 Horz. Asym.: y = 1 Domain: All reals except 0 Range: All reals except 1
8 6 4
6 4
2 −8
−6
−4
9) f ( x) = −
2
−2
2
4
6
8 x
−8
−6
−4
−2 −2
−4
−4
−6
−6
−8
−8
4 +1 x+1
10) f ( x) =
y
4
−2
6
8 x
y
Vertical Asym.: x = 0 Horz. Asym.: y = 2 Domain: All reals except 0 Range: All reals except 2
8 6 4
2 −4
4
4 +2 x
Vertical Asym.: x = −1 Horz. Asym.: y = 1 Domain: All reals except −1 Range: All reals except 1
6
−6
2
−2
8
−8
Vertical Asym.: x = 3 Horz. Asym.: y = 1 Domain: All reals except 3 Range: All reals except 1
8
2 2
4
6
8 x
−8
−6
−4
−2
2
−2
−2
−4
−4
−6
−6
−8
−8
4
6
8 x
Critical thinking question: 11) Write a function of the form f ( x) = Many answers. Ex: f ( x) =
a + k with a vertical asymptote at x = 25 x−h
1 x − 25
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
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