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Math 1330, Precalculus
2. Neither 4. Even 6. Odd 8. (a)
(b)
10. (a) Hole: at x = 2
(b) x- intercept: 0 (c) y- intercept: 0 (d) Vertical Asymptotes: x = − 3 , x = 3 (e) Horizontal Asymptote: y =− 2
12. (a) Domain: ( −∞ −, 7 )∪( 7,− ∞)
(b) Hole(s): None (c) x- intercept(s): None (d) y- intercept: − 74
(e) Vertical Asymptote: x =− 7
Continued in the next column…
(f) Horizontal Asymptote: y = 0 (g) Slant Asymptote(s): None (h) Graph:
14. (a) Domain: ( −∞, 0 ) ∪(0, ∞)
(b) Hole(s): None (c) x- intercept: 49 (d) y- intercept(s): None (e) Vertical Asymptote: x = 0 (f) Horizontal Asymptote: y =− 4 (g) Slant Asymptote(s): None (h) Graph:
16. (a) Domain: ( −∞, 2 )∪(2, ∞)
(b) Hole(s): None (c) x- intercept(s): − 5 (d) y- intercept(s): − 25 (e) Vertical Asymptote: x = 2 (f) Horizontal Asymptote: y = 1 (g) Slant Asymptote(s): None (h) Graph:
−6 −4 −2 2 4 6
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−6 −4 −2 2 4 6
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−14 −12 −10 −8 −6 −4 −2 2
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−6 −4 −2 2 4 6
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−6 −4 −2 2 4 6 8
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Math 1330, Precalculus
−4 −2 2 4 6 −
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−6 −4 −2 2 4 6
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18. (a) Domain: ( −∞, 12 )∪( 12 , ∞)
(b) Hole(s): None (c) x- intercept: − 2 (d) y- intercept: − 6 (e) Vertical Asymptote: x = 21
(f) Horizontal Asymptote: y = 23 (g) Slant Asymptote(s): None (h) Graph:
20. (a) Domain: ( −∞ −, 3 ) ∪ ( 3, 2)− ∪(2, ∞)
(b) Hole: at x =− 3 (c) x- intercept: 6 (d) y- intercept: − 3 (e) Vertical Asymptote: x = 2 (f) Horizontal Asymptote: y =− 1 (g) Slant Asymptote(s): None (h) Graph:
22. (a) Domain: ( −∞, 5 ) ∪(5, ∞)
(b) Hole: at x = 5 (c) x- intercept: − 2 (d) y- intercept: 2 (e) Vertical Asymptote(s): None (f) Horizontal Asymptote(s): None
Continued in the next column…
(g) Slant Asymptote(s): None (Note: There is no slant asymptote when the remainder after performing long division is zero. The graph of this function is simply a line with a removable discontinuity / hole at x = 5 .) (h) Graph:
24. (a) Domain: ( −∞ −, 3 ) ∪ ( 3, 3)− ∪(3, ∞)
(b) Hole(s): None (c) x- intercept: 0 (d) y- intercept: 0 (e) Vertical Asymptote: x = −3, x = 3 (f) Horizontal Asymptote: None (g) Slant Asymptote(s): y =^12 x (h) Graph:
26. (a) Domain: ( −∞ −, 4 )∪ ( 4, 3)− ∪(3, ∞)
(b) Hole: at x =− 4 (c) x- intercept: 57
(d) y- intercept: − 37
(e) Vertical Asymptote: x = 3 (f) Horizontal Asymptote: y =− 5
Continued on the next page…
−4 −2 2 4 6 8 10
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−8 −6 −4 −2 2 4 6
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Math 1330, Precalculus
−6 −4 −2 2 4 6
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(h) Graph:
36. (a) Domain: ( −∞ −, 5 ) ∪ ( 5,− − 3) ∪ ( 3, 3)− ∪(3, ∞)
(b) Hole: at x =− 5 (c) x- intercept: 0 (d) y- intercept: 0 (e) Vertical Asymptotes: x = − 3 , x = 3 (f) Horizontal Asymptote: y = 2 (g) Slant Asymptote(s): None (h) Graph:
38. (a) Domain: ( −∞, 2 )∪ (2, 4) ∪(4, ∞)
(b) Holes: at x = 2 and x = 4 (c) x- intercepts: 3 , − 1 (d) y- intercept: 3 (e) Vertical Asymptote(s): None (f) Horizontal Asymptote(s): None (g) Slant Asymptote(s): None (h) Graph:
40. (a) Domain: ( −∞, 0 ) ∪(0, ∞)
(b) Hole(s): None (c) x- intercepts: −3, −1, 1, 3 (d) y- intercept(s): None (e) Vertical Asymptote: x = 0 (f) Horizontal Asymptote(s): None (g) Slant Asymptote: y = x (h) Graph:
42. (a) x -intercepts:
x = − ± ;
x ≈ − 3.6; x ≈0. (b) Vertical Asymptotes: x = 3 − 5; x = 3 + 5 x ≈ 0.8; x ≈5, 2
44. (a) y = 1 (b) x = − 1
(c) ( −1, 1)
46. (a) y^ =^3 (b) x = − 1
(c) ( −1, 3)
48. (a)
y =
(b)
x =
(c)
−8 −6 −4 −2 2 4 6 8
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−6 −4 −2 2 4 6
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−8 −6 −4 −2 2 4 6 8
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Math 1330, Precalculus
50. (a) ( −2, 0)
(b)
−8 −6 −4 −2 2 4 6 8
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