College Algebra, 2013a

412 Further Topics in Functions
√
16x
5. f(x) = 4 x 2 − 9
Domain: (−3, 0] ∪ (3, ∞)
(+)
(+)
”
−3
0 ”
0
Vertical asymptotes: x = −3 andx =3
Horizontal asymptote: y =0
Unusual steepness at x =0
No cusps
3
y
5
4
3
2
1
−3 −2 −1 1 2 3 4 5 6 7 8
x
5x
6. f(x) = 3√
x 3 +8
Domain: (−∞, −2) ∪ (−2, ∞)
(+) ” (−) 0 (+)
−2
Vertical asymptote x = −2
Horizontal asymptote y =5
No unusual steepness or cusps
0
8
7
6
5
4
3
2
1
−4−3−2−1 −1 1 2 3 4
−2
−3
−4
−5
−6
y
x
7. f(x) =x 2 3 (x − 7) 1 3
Domain: (−∞, ∞)
(−) 0 (−)
0
0 (+)
No vertical or horizontal asymptotes 13
Unusual steepness at x =7
Cusp at x =0
7
y
5
4
3
2
1
−3−2−1
−1
1 2 3 4 5 6 7 8 9
−2
−3
−4
x
8. f(x) =x 3 2 (x − 7) 1 3
Domain: [0, ∞)
0 (−)
0
0 (+)
7
No asymptotes
Unusual steepness at x =7
No cusps
25
20
15
10
5
−5
−10
−15
y
1 2 3 4 5 6 7 8 x
13 Using Calculus it can be shown that y = x − 7 is a slant asymptote of this graph.
3