Logarithms And Logarithmic Functions Worksheet With Answers Page 21
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27ANSWER:
c .
No; Elisa was closer. She should have –y = 2 or y =
d . log
1 = 0;
–2 instead of y = 2. Matthew used the definition of
7-3 Logarithms and Logarithmic Functions
7
e . There is no possible solution; this is the empty set.
logarithms incorrectly.
65. FIND THE ERROR Elisa and Matthew are
66. WRITING IN MATH A transformation of log
x
10
evaluating
Is either of them correct? Explain
is g(x) = alog
(x − h) + k. Explain the process of
10
graphing this transformation.
your reasoning.
SOLUTION:
Sample answer: In g(x) = alog
(x − h) + k, the
10
value of k is a vertical translation and the graph will
shift up k units if k is positive and down |k| units if k
is negative. The value of h is a horizontal translation
and the graph will shift h units to the right if h is
positive and |h| units to the left if h is negative. If a <
0, the graph will be reflected across the x-axis. if |a|
> 1, the graph will be expanded vertically and if 0 <
|a| < 1, then the graph will be compressed vertically.
ANSWER:
Sample answer: In g(x) = alog
(x − h) + k, the
10
value of k is a vertical translation and the graph will
shift up k units if k is positive and down |k| units if k
is negative. The value of h is a horizontal translation
and the graph will shift h units to the right if h is
positive and |h| units to the left if h is negative. If a <
0, the graph will be reflected across the x-axis. if |a|
> 1, the graph will be expanded vertically and if 0 <
|a| < 1, then the graph will be compressed vertically.
67. A rectangle is twice as long as it is wide. If the width
of the rectangle is 3 inches, what is the area of the
rectangle in square inches?
A 9
B 12
C 15
SOLUTION:
D 18
No; Elisa was closer. She should have –y = 2 or y =
–2 instead of y = 2. Matthew used the definition of
SOLUTION:
logarithms incorrectly.
Length of the rectangle = 2 * 3 = 6 inches.
Area of the rectangle = 6 * 3 = 18 square inches.
ANSWER:
D is the correct option.
No; Elisa was closer. She should have –y = 2 or y =
ANSWER:
–2 instead of y = 2. Matthew used the definition of
logarithms incorrectly.
D
66. WRITING IN MATH A transformation of log
x
68. SAT/ACT Ichiro has some pizza. He sold 40% more
10
slices than he ate. If he sold 70 slices of pizza, how
is g(x) = alog
(x − h) + k. Explain the process of
10
many did he eat?
graphing this transformation.
F 25
G 50
SOLUTION:
H 75
Sample answer: In g(x) = alog
(x − h) + k, the
10
J 98
value of k is a vertical translation and the graph will
K 100
shift up k units if k is positive and down |k| units if k
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Page 21
is negative. The value of h is a horizontal translation
SOLUTION:
and the graph will shift h units to the right if h is
Let x be the number of pizza slices Ichiro ate.
positive and |h| units to the left if h is negative. If a <
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