Name :

Teacher : Date :

Score :

Math-Aids.Com

Graphing General Rational FunctionsGraphing General Rational FunctionsFind the vertical and horizontal asymptotes as well as the domain and range.

1)- 1

x2 - 4 x

_____ 2)- 3

x + 2

____

3)x - 2

- 4 x - 16

_______ 4)x

3 - 4 x

x2 - 7 x + 12

_________

5)1

x - 2

___ + 2 6)- 3

x - 3

___

7)x

3 - 16 x

x2 + x - 6

_______ 8)- 2

x

__ + 1

Name :

Teacher : Date :

Score :

Math-Aids.Com

Graphing General Rational FunctionsGraphing General Rational FunctionsGraph the given function

9)x

3 + x

2 - 6 x

x2 - 2 x - 8

_________

>X<

AY

V

-10 1-9 2-8 3-7 4-6 5-5 6-4 7-3 8-2 9-1 10

1

-10

2

-9

3

-8

4

-7

5

-6

6

-5

7

-4

8

-3

9

-2

10

-1

10)2

x

_

>X<

AY

V

-10 1-9 2-8 3-7 4-6 5-5 6-4 7-3 8-2 9-1 10

1

-10

2

-9

3

-8

4

-7

5

-6

6

-5

7

-4

8

-3

9

-2

10

-1

11)- 2

x2 + 2 x

______

>X<

AY

V

-10 1-9 2-8 3-7 4-6 5-5 6-4 7-3 8-2 9-1 10

1

-10

2

-9

3

-8

4

-7

5

-6

6

-5

7

-4

8

-3

9

-2

10

-1

12)- 3

x - 4

___ - 3

>X<

AY

V

-10 1-9 2-8 3-7 4-6 5-5 6-4 7-3 8-2 9-1 10

1

-10

2

-9

3

-8

4

-7

5

-6

6

-5

7

-4

8

-3

9

-2

10

-1

Name :

Teacher : Date :

Score :

Math-Aids.Com

Graphing General Rational FunctionsGraphing General Rational FunctionsFind the vertical and horizontal asymptotes as well as the domain and range.

1)- 1

x2 - 4 x

_____

Discontinuities: 0, 4

Horiz. Asym. : y = 0

Vert. Asym. : x = 0, x = 4

Holes: None

X Ints. : None

2)- 3

x + 2

____

Discontinuities: -2

Horiz. Asym. : y = 0

Vert. Asym. : x = -2

Holes: None

X Ints. : None

3)x - 2

- 4 x - 16

_______

Discontinuities: -4

Horiz. Asym. : y = 1-4__

Vert. Asym. : x = -4

Holes: None

X Ints. : 2

4)x

3 - 4 x

x2 - 7 x + 12

_________

Discontinuities: 4, 3

Horiz. Asym. : None

Vert. Asym. : x = 4, x = 3

Holes: None

X Ints. : 0, 2, -2

5)1

x - 2

___ + 2

Discontinuities: 2

Horiz. Asym. : y = 2

Vert. Asym. : x = 2

Holes: None

X Ints. : None

6)- 3

x - 3

___

Discontinuities: 3

Horiz. Asym. : y = 0

Vert. Asym. : x = 3

Holes: None

X Ints. : None

7)x

3 - 16 x

x2 + x - 6

_______

Discontinuities: -3, 2

Horiz. Asym. : None

Vert. Asym. : x = -3, x = 2

Holes: None

X Ints. : 0, 4, -4

8)- 2

x

__ + 1

Discontinuities: 0

Horiz. Asym. : y = 1

Vert. Asym. : x = 0

Holes: None

X Ints. : None

Find the vertical and horizontal asymptotes as well as the domain and range.

Name :

Teacher : Date :

Score :

Math-Aids.Com

Graphing General Rational FunctionsGraphing General Rational Functions

9)x

3 + x

2 - 6 x

x2 - 2 x - 8

_________

>X<

AY

V

-10 1-9 2-8 3-7 4-6 5-5 6-4 7-3 8-2 9-1 10

1

-10

2

-9

3

-8

4

-7

5

-6

6

-5

7

-4

8

-3

9

-2

10

-1

10)2

x

_

>X<

AY

V

-10 1-9 2-8 3-7 4-6 5-5 6-4 7-3 8-2 9-1 10

1

-10

2

-9

3

-8

4

-7

5

-6

6

-5

7

-4

8

-3

9

-2

10

-1

11)- 2

x2 + 2 x

______

>X<

AY

V

-10 1-9 2-8 3-7 4-6 5-5 6-4 7-3 8-2 9-1 10

1

-10

2

-9

3

-8

4

-7

5

-6

6

-5

7

-4

8

-3

9

-2

10

-1

12)- 3

x - 4

___ - 3

>X<

AY

V

-10 1-9 2-8 3-7 4-6 5-5 6-4 7-3 8-2 9-1 10

1

-10

2

-9

3

-8

4

-7

5

-6

6

-5

7

-4

8

-3

9

-2

10

-1