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**Unformatted text preview: **ath for x ≥ 0. What is the signiﬁcance
of the y -intercept of the graph?
(b) Determine the path Fritzy will take if Chewbacca runs exactly twice as fast as he does;
that is, v1 = 2v2 . Use your calculator to graph this path for x > 0. Describe the behavior
of y as x → 0+ and interpret this physically.
(c) With the help of your classmates, generalize parts (a) and (b) to two cases: v2 > v1 and
v2 < v1 . We will discuss the case of v1 = v2 in Exercise 10 in Section 6.5. 324 5.3.2 Further Topics in Functions Answers √
1. (a) f (x) = 1 − x2
Domain: [−1, 1]
(+)
0 y 0 1 −1
1
No asymptotes
Unusual steepness at x = −1 and x = 1
No cusps −1 1 x y 16x
(b) f (x) =
x2 − 9
Domain: (−3, 0] ∪ (3, ∞)
(+)
(+) 0
4 5
4
3 −3
0
3
Vertical asymptotes: x = −3 and x = 3
Horizontal asymptote: y = 0
Unusual steepness at x = 0
No cusps
2 1
−3 −2 −1 2 3 4 5 6 5
4
3
2 0
7
No vertical or horizontal asymptotes12
Unusual steepness at x = 7
Cusp at x = 0 1
−3 −2 −1
−1 1 2 3 4 5 6 1 2 3 4 x −2
−3
−4 y 5x
x3 + 8
Do...

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