Name : Teacher : Date : Score : Math-Aids.Com Graphing General Rational Functions Graphing General Rational Functions Find the vertical and horizontal asymptotes as well as the domain and range. 1) - 1 x 2 - 4 x _____ 2) - 3 x + 2 ____ 3) x - 2 - 4 x - 16 _______ 4) x 3 - 4 x x 2 - 7 x + 12 _________ 5) 1 x - 2 ___ + 2 6) - 3 x - 3 ___ 7) x 3 - 16 x x 2 + x - 6 _______ 8) - 2 x __ + 1
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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
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