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4. hole at x 2; large and negative to
left of asymptote, large and positive to
right of asymptote;
y 1;
Domain: 5xR 0 x 2, x 36
5.
y
6. There are discontinuities at x 3
and x 3.
7.
lim f 1x2 q
xS3
x 3 is a vertical
f 1x2 q asymptote.
lim
xS3
20
–6 –4 –2
0
2 4 6 8 10
–20
–40
–60
–80
–100
–120
–140
lim f 1x2 q
xS3
is a vertical
lim f 1x2 q asymptote.
x 3
xS3
The y-intercept is 10 and x-intercept
9
is 5.
Q9, 1 is a local minimum and
9 R
11, 12 is a local maximum.
y 0 is a horizontal asymptote.
8
6
4
2
–10 –8 –6 –4 –2
0
–2
–4
–6
–8
2 4 6 8 10
b 3, c 2
y
8
(–2, 6)
6
4
2
(0, 2)
–4 –3 –2 –1
0
1 2 3 4
–2
–4
–6
–8
y
x
x
x
Chapter 5
Review of Prerequisite Skills,
pp. 224–225
1. a.
1
1
c.
9
9
b. 4
9
d.
4
2. a. log 5 625 4
b. log 1 4
16 2
c. log x 3 3
d. log 10 450 w
e.
f.
log 3 z 8
log a T b
3. a.
y
3
2
1
–3 –2 –1
0
–1
–2
–3
x-intercept: 11, 02
b.
y
10
–8 –6 –4 –2 0
–2
no x-intercept
4. a.
y
x y
b. c.
r
r x
5. a. 2p
3p
e.
2
b.
p
4
f. 2p 3
c.
5p
p g.
2
4
p
11p
d. h.
6
6
6. a. b c. a e. b
b.
b
a
d. a f. b
7. a. cos u 12 ,
13
tan u 5 12
8
6
4
2
1
2 3
x
2 4 6
8
x
b. sin u 5 ,
3
c. sin u 2 ,
5
cos u
1 5
p
d. cos ,
2 0
p
tan is undefined
2
8. a. period: p,
amplitude: 1
b. period: 4p,
amplitude: 2
c. period: 2,
amplitude: 3
p
d. period: ,
6
2
amplitude:
7
e. period: 2p,
amplitude: 5
f. period: 2p,
3
amplitude:
2
9. a. y
4
b.
tan u 5
2
3
2
1
3
2
1
0
– 1
–2
–3
0
y
p
2
p
p
2
10. a. tan x cot x sec x csc x
LS tan x cot x
sin x
cos x cos x
sin x
3p
2
3p
2
2p 5p 3p 7p x
2 2
2p
sin2 x cos 2 x
cos x sin x
1
cos x sin x
RS sec x csc x
1
cos x 1
sin x
1
cos x sin x
Therefore, tan x cot x
sec x csc x.
p
x
NEL
Answers 653