Algebra 2
Name___________________________________ ID: 1
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HW 6: Graphing Rational Functions
Date________________ Period____
Identify the holes, vertical asymptotes, x-intercepts, horizontal asymptote, and domain of each. Then sketch the graph. 1) f ( x) =
x 2 - 5x + 4 4x 2 - 4
2) f ( x) =
x 3 + 2x 2 - 8x -3x 2 - 3x
y
-8
-6
-4
3) f ( x) = -
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
4
6
8 x
3 x -4 2
y 8 6 4 2 -8
-6
-4
-2
2
4
6
8 x
-2 -4 -6 -8
Worksheet by Kuta Software LLC
-1-
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4) f ( x) =
x 2 + 4x + 3 -2x 2 - 10x - 12
5) f ( x) =
3x 2 - 6x x 3 - 5x 2 + 6x
y
-8
-6
-4
f ( x) =
6)
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
x 2 + 3x + 2 -3x 2 + 12
-6
-4
8 x
6
8 x
2
7)
x + 4x + 3 y
8
8
6
6
4
4
2
2
-2
6
-2x - 14x - 24 f ( x) = 2
y
-8
4
2
4
6
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
Worksheet by Kuta Software LLC
-2-
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8) f ( x) =
x 3 - 9x -4x 2 + 16 y 8 6 4 2
-8
-6
-4
-2
2
4
6
8 x
-2 -4 -6 -8
9) f ( x) =
x-3 2x 2 - 18
10) f ( x) =
-3x + 12 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
4
6
8 x
Worksheet by Kuta Software LLC
-3-
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Answers to HW 6: Graphing Rational Functions (ID: 1) 1)
2)
y 8 6 4 2 -8 -6 -4 -2
2
4
6
Vertical Asym.: x = -1 Holes: x = 1 1 Horz. Asym.: y = 4 X-intercepts: 4 Domain: 8 x All reals except -1, 1
y 6 4 2 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
3)
4)
y 6 4 2 -8 -6 -4 -2
2
4
6
8 x
-8 -6 -4 -2
2 -4 -6
-8
-8
6)
2 -8 -6 -4 -2
2
4
6
6 4 2
8 x
-8 -6 -4 -2
2 -2
-4
-4
-6
-6
-8
-8
8)
y 6 4 2 -8 -6 -4 -2
2
4
6
6 4 2
8 x
-8 -6 -4 -2
2 -2
-4
-4
-6
-6
-8
-8
10)
y 6 4 2 -8 -6 -4 -2
2
4
6
4
8 x
6
y
Vertical Asym.: x = -3 Holes: x = 3 Horz. Asym.: y = 0 X-intercepts: None Domain: All reals except -3, 3
8
Vertical Asym.: x = 2, x = -2 Holes: None Horz. Asym.: None X-intercepts: 0, 3, -3 Domain: All reals except 2, -2
8
-2
9)
4
y
Vertical Asym.: x = -1 Holes: x = -3 Horz. Asym.: y = -2 X-intercepts: -4 Domain: All reals except -1, -3
8
6
8
-2
7)
4
y
Vertical Asym.: x = 3 Holes: x = 0, x = 2 Horz. Asym.: y = 0 X-intercepts: None Domain: All reals except 3, 0, 2
4
Vertical Asym.: x = 2 Holes: x = -2 1 Horz. Asym.: y = 3 X-intercepts: -1 Domain: 8 x All reals except 2, -2
2
-6
6
6
Vertical Asym.: x = -2 Holes: x = -3 1 Horz. Asym.: y = 2 X-intercepts: -1 Domain: 8 x All reals except -2, -3
4
-4
y
8 x
6
-2
8
6
8
-2
5)
4
y
Vertical Asym.: x = 2, x = -2 Holes: None Horz. Asym.: y = 0 X-intercepts: None Domain: All reals except 2, -2
8
Vertical Asym.: x = -1 Holes: x = 0 Horz. Asym.: None X-intercepts: 2, -4 Domain: All reals except -1, 0
8
Vertical Asym.: x = 1 Holes: None Horz. Asym.: y = -3 X-intercepts: 4 Domain: All reals except 1
8 6 4 2
8 x
-8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8 x
Worksheet by Kuta Software LLC
-4-
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