Worksheet by Kuta Software LLC ... GRAPHING RATIONAL FUNCTIONS ... Then
sketch the graph. 1) f (x) = x − 4. −3x. 2 − 3x + 18 x y. −8. −6. −4. −2. 2. 4. 6. 8.
2A/Trig
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GRAPHING RATIONAL FUNCTIONS ©v h220r1W0t yK2u1tHaL 6S1oMfPtqwnaOroee ULYLXCG.y o rAflilO brIiCg3hStJsq vrOeysrear2vhezdB.T
Identify the holes, vertical asymptotes, x-intercepts, horizontal asymptote, and domain of each. Then sketch the graph. 1) f ( x) =
x−4 −3 x − 3 x + 18 8
−8
−6
−4
3) f ( x) =
−6
y
8 6
4
4
2
2
−2
2
4
6
8 x
−8
−6
−4
2 −2
−4
−4
−6
−6
−8
−8
4) f ( x) = y
8 6
4
4
2
2 2
4
6
8 x
−8
−6
−4
−2 −2
−4
−4
−6
−6
−8
−8
-1-
6
8 x
6
8 x
y
2
−2
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4
x3 − 4x2 −4 x 3 + 4 x 2 + 48 x
6
−2
y
−2
−2
x 2 x + 4x
−4
x −x + 2x2 + 3x 3
6
8
−8
2) f ( x) =
2
4
Worksheet by Kuta Software LLC
5) f ( x) =
x2 + 6x + 8 −4 x − 12 8
−8
−6
−4
7) f ( x) =
−6
9) f ( x) =
−6
8 6
4
4
2
2
−2
2
4
6
8 x
−6
−4
2
−4
−4
−6
−6
−8
−8
8) f ( x) =
8
6
6
4
4
2
2 2
4
6
8 x
−8
−6
−4
−2
−4
−4
−6
−6
−8
−8
10) f ( x) =
8
6
6
4
4
2
2 4
6
8 x
−8
−6
−4
−2
−2
−2
−4
−4
−6
−6
−8
−8
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-2-
8 x
2
4
6
8 x
2
4
6
8 x
x2 − x −3 x − 3
y
2
6
y
−2
−2
−2
4
x3 − 5x2 + 4x −3 x 2 + 12 x − 9
y
−2
y
−2 −2
x 3 − 16 x 2 x 2 − 18
−4
−8
−2
8
−8
y
x 2 − 16 4x + 4
−4
x 3 − 7 x 2 + 12 x 4 x 2 − 20 x + 24
6
8
−8
6) f ( x) =
y
Worksheet by Kuta Software LLC
Answers to GRAPHING RATIONAL FUNCTIONS 1) 8
2)
y
6 4 2 −8 −6 −4 −2
2
−2
4
6
8 x
−8 −6 −4 −2
−8
4)
2 2
−2
4
6
8 x
Vertical Asym.: x = −4 Holes: x = 0 Horz. Asym.: y = 0 X-intercepts: None Domain: All reals except −4, 0
8
−6
−8
−8
6)
6 4 2 2
−2
4
6
8 x
Vertical Asym.: x = −3 Holes: None Horz. Asym.: None X-intercepts: −2, −4 Domain: All reals except −3
8
−8 −6 −4 −2
−6 −8
8)
4 2 2
−2
4
6
8 x
Vertical Asym.: x = −1 Holes: None Horz. Asym.: None X-intercepts: −4, 4 Domain: All reals except −1
8
−8 −6 −4 −2
−6 −8
2
10)
4 2 −2
y
−2
−8
6
2
4
6
8 x
Vertical Asym.: x = −3, x = 3 Holes: None Horz. Asym.: None X-intercepts: 0, −4, 4 Domain: All reals except −3, 3
8
4
6
8 x
Vertical Asym.: x = 2 Holes: x = 3 Horz. Asym.: None X-intercepts: 0, 4 Domain: All reals except 2, 3
Vertical Asym.: x = 3 Holes: x = 1 Horz. Asym.: None X-intercepts: 0, 4 Domain: All reals except 3, 1
y
6 4 2 −8 −6 −4 −2
−2
−4
−4
−6
−6
−8
−8
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8 x
2
−4
y
6
4
−6
8
4
6
−4
9)
2
−2
−8
6
y
2
−4
8
4
4
−6
y
2
6
−4
7)
6
Vertical Asym.: x = −3 Holes: x = 0, x = 4 1 Horz. Asym.: y = − 4 X-intercepts: None Domain: 8 x All reals except −3, 0, 4
y
−2 −4
y
8 x
2 −8 −6 −4 −2
Vertical Asym.: x = 3, x = −1 Holes: x = 0 Horz. Asym.: y = 0 X-intercepts: None Domain: All reals except 3, −1, 0
6
4
−6
8
4
6
−4
5)
2
−2 −6
4
−8 −6 −4 −2
2
−8
6
−8 −6 −4 −2
4
−4
y
y
6
−6
8
−8 −6 −4 −2
8
−4
3)
−8 −6 −4 −2
Vertical Asym.: x = 2, x = −3 Holes: None Horz. Asym.: y = 0 X-intercepts: 4 Domain: All reals except 2, −3
-3-
2
4
6
8 x
Vertical Asym.: x = −1 Holes: None Horz. Asym.: None X-intercepts: 0, 1 Domain: All reals except −1
Worksheet by Kuta Software LLC
