Graphing Simple Rational Functions - Kuta Software

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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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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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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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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Worksheet by Kuta Software LLC