Chapter 8

c) x 5 Q 1 y
or f 21 (x) 5 log A
1
3 R 3Bx
4
3
2
1
4
3
2
1
y
–1
0
1 2 3 4
–1
d) x 5 Q 1 y
or f 21 (x) 5 log A
1
5 R 5Bx
y
–1
0
1 2 3 4
–1
2. a) i) x 5 4 y
ii) log 4 x 5 y
b) i) x 5 8 y
ii) log 8 x 5 y
c) i) x 5 a 1 y
3 b
ii) log 1
3
d) i) x 5 a 1 y
5 b
ii) log 1
5
3. All the graphs have the same basic shape,
but the last two are reflected over the x-axis,
compared with the first two. All the graphs
have the same x-intercept, 1. All have the
same vertical asymptote, x 5 0.
4. Locate the point on the graph that has 8
as its x-coordinate. This point is (8, 3).
The y-coordinate of this point is the
solution to 2 y 5 8, y 5 3.
5. a) x 5 3 y c) x 5 a 1 y
4 b
b) x 5 10 y d) x 5 m y
6. a) 3x 5 y c) log 1
4
b) log x 5 y 10 d) log x 5 y m
7. a) x 5 5 y c) x 5 3 y
8. a) y 5 5 x c) y 5 3 x
b) x 5 10 y d) x 5 1 y
4
b) y 5 10 x d) y 5 1 x
4
9. a) 2 d) 0
b) 3 e) 21
1
c) 4 f)
2
10. Since 3 is positive, no exponent for 3 x can
produce 29.
11. a) a1 , a 1 , (1, 0) , (2, 1) , (4, 2)
4 , 22b 2 , 21b
b) a 1 , a 1 , (1, 0) ,
100 , 22b 10 , 21b
(10, 1) , (100, 2)
x
x
Lesson 8.2, pp. 457–458
1. a) vertical stretch by a factor of 3
1
b) horizontal compression by a factor of
2
c) vertical translation 5 units down
d) horizontal translation 4 units left
2. a) (a) a 1 , (1, 0) , (10, 3)
10 , 23b
(b) a 1 , a 1 , (5, 1)
20 , 21b 2 , 0b
(c) a 1 , (1, 25) , (10, 24)
10 , 26b
(d) a23 9 , (23, 0) , (6, 1)
10 , 21b
b) (a) D 5 5xPR 0 x . 06,
R 5 5 yPR6
(b) D 5 5xPR 0 x . 06,
R 5 5 yPR6
(c) D 5 5xPR 0 x . 06,
R 5 5 yPR6
(d) D 5 5xPR 0 x .246,
R 5 5 yPR6
3. a) f (x) 5 5 log 10 x 1 3
b) f (x) 52log 10 (3x)
c) f (x) 5 log 10 (x 1 4) 2 3
d) f (x) 52log 10 (x 2 4)
4. i) a) reflection in the x-axis and a vertical
stretch by a factor of 4; c 5 5
resulting in a translation 5 units up
b) (1, 5) , (10, 1)
c) vertical asymptote is x 5 0
d) D 5 5xPR 0 x . 06,
R 5 5 yPR6
1
ii) a) vertical compression by a factor of ;
2
d 5 6 resulting in a horizontal
translation 6 units to the right; c 5 3
resulting in a vertical translation
3 units up
b) (7, 3) , a16, 3 1 2 b
c) vertical asymptote is x 5 6
d) D 5 5xPR 0 x . 66,
R 5 5 yPR6
iii) a) horizontal compression by a factor
1
of c 524 resulting in a vertical
3 ;
shift 4 units down
b) a1 , a3 1 3 , 24b 3 , 23b
c) vertical asymptote is x 5 0
d) D 5 5xPR 0 x . 66,
R 5 5 yPR6
iv) a) vertical stretch by a factor of 2;
k 522 resulting in a horizontal
1
compression by a factor of and a
2
reflection in the y-axis; d 522
resulting in a horizontal translation
2 units to the left.
b) a22 1 , (27, 2)
2 , 0b
c) vertical asymptote is x 522
d) D 5 5xPR 0 x ,226,
R 5 5 yPR6
v) a) horizontal compression by a factor of
1
; d 522 resulting in a horizontal
2
translation 2 units to the left
b) a21 1 , (3, 1)
2 , 0b
c) vertical asymptote is x 522
d) D 5 5xPR 0 x .226,
R 5 5 yPR6
vi) a) reflection in the x-axis; d 522,
resulting in a horizontal translation
2 units to the right
b) (23, 0) , (212, 1)
c) vertical asymptote is x 522
d) D 5 5xPR 0 x ,226,
R 5 5 yPR6
5. a) D 5 5xPR 0 x . 06,
R 5 5 yPR6
y
5
x
0
5 10 15
–5
–10
b) D 5 5xPR 0 x .266,
R 5 5 yPR6
y
10
5
x
0
5 10 15
–5
c) D 5 5xPR 0 x . 06,
R 5 5 yPR6
y
5
x
0
5 10 15
–5
–10
668 Answers
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