AnswersMDVA Algebra II Sem. 2Unit Test

Unit Test — Unit test Answers

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The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as , where and is the least intense sound a human ear can hear. What is the approximate loudness of a rock concert with a sound intensity of 10–1?

Question illustration
A
2 Db
B
22 Db
C
60 Db
D
110 Db
2
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What is the solution of log2 (3x - 7) = 3?

A
One-third
Option A
B
4
C
5
D
Sixteen-thirds
Option D
3

Which expression is equivalent to ?

Question illustration
A
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1)
Option A
B
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline StartFraction x cubed Over 2 EndFraction minus 5 log Subscript 12 Baseline 1
Option B
C
log Subscript 12 Baseline 4 x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x) + 1
Option C
D
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x + 1)
Option D
4

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

Question illustration
A
–1.5
B
–0.5
C
1.5
D
3.6
5

If you are given the graph of , how could you graph ?

Question illustration
A
Translate each point of the graph of h(x) 3 units up.
B
Translate each point of the graph of h(x) 3 units down.
C
Translate each point of the graph of h(x) 3 units right.
D
Translate each point of the graph of h(x) 3 units left.
6

Which equation is represented by the graph below?

Question illustration
A
y = l n x minus 3
Option A
B
y = l n x minus 4
Option B
C
y = e Superscript x Baseline minus 3
Option C
D
y = e Superscript x Baseline minus 4
Option D
7

Which of the following is true about the base b of a logarithmic function?

A
b > 0 and b = 1
B
b > 0 and
Option B
C
b < 0 and
Option C
D
b < 0 and b = 1
8

What is the true solution to the logarithmic equation below?

Question illustration
A
x = 0
Option A
B
x = two-ninths
Option B
C
x = four-ninths
Option C
D
x = two-thirds
Option D
9

What is the solution to

Question illustration
A
x = negative 4
Option A
B
x = negative 2
Option B
C
x = 4
Option C
D
x = 8
Option D
10

Which graph shows the solution to the equation below?

Question illustration
A
On a coordinate plane, 2 curves intersect at (1, 0).
Option A
B
On a coordinate plane, a line intersects with a curve.
Option B
C
On a coordinate plane, a line with positive slope and a curve are shown.
Option C
D
On a coordinate plane, 2 hyperbolas are shown.
Option D
11

What is the true solution to the equation below?

Question illustration
A
x = 2
Option A
B
x = 4
Option B
C
x = 8
Option C
D
x = 64
Option D
12

How does the value of compare with the value of ?

Question illustration
A
The value of is about 4 times the value of .
Option A
B
The value of is about times the value of .
Option B
C
The value of is about 3 times the value of .
Option C
D
The value of is about times the value of .
Option D
13

Which of the following shows the graph of y = 4x + 3?

A
On a coordinate plane, an exponential function starts at y = 3 in quadrant 2 and then increases rapidly into quadrant 1.
Option A
B
On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly in quadrant 2.
Option B
C
On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly into quadrant 1.
Option C
D
On a coordinate plane, an exponential function starts at y = negative 3 in quadrant 3 and then increases rapidly into quadrant 1.
Option D
14

The range of which function is ?

Question illustration
A
y = 2x
B
y = 2(5x)
C
y = 5x +2
D
y = 5x + 2
15

Which graph represents an exponential decay function?

A
On a coordinate plane, a curve opens up and to the right in quadrant 4.
Option A
B
On a coordinate plane, a curve opens up and to the right in quadrants 1 and 2. The line rapidly decreases in quadrant 2 and then curves and approaches the x-axis in quadrant 1.
Option B
C
On a coordinate plane, a line slightly curves up in quadrant 1.
Option C
D
On a coordinate plane, a line slowly increases in quadrant 2 and then increases rapidly into quadrant 1.
Option D
16

Which function is shown in the graph below?

Question illustration
A
y = (one-half) Superscript x + 3 Baseline minus 1
Option A
B
y = (one-half) Superscript x minus 3 Baseline + 1
Option B
C
y = (one-half) Superscript x minus 1 Baseline + 3
Option C
D
y = (one-half) Superscript x + 1 Baseline minus 3
Option D
17

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as , where and is the least intense sound a human ear can hear. Jessica is listening to soft music at a sound intensity level of 10-9 on her computer while she does her homework. Braylee is completing her homework while listening to very loud music at a sound intensity level of 10-3 on her headphones. How many times louder is Braylee’s music than Jessica’s?

Question illustration
A
times louder
Option A
B
3 times louder
C
30 times louder
D
90 times louder
18

What is the approximate value of ?

Question illustration
A
0.233
B
0.557
C
0.620
D
1.796
19

Which is the graph of ?

Question illustration
A
On a coordinate plane, a curve starts at y = negative 3 and curves up into quadrant 1. It approaches y = 3.
Option A
B
On a coordinate plane, a curve starts at y = negative 2 and curves up into quadrant 2. It approaches y = 2 in quadrant 2.
Option B
C
On a coordinate plane, a curve starts at y = 3 and curves down into quadrant 4. It approaches y = negative 3 in quadrant 4.
Option C
D
On a coordinate plane, a curve starts at y = 4 and curves down into quadrant 3. It approaches y = negative 3 in quadrant 3.
Option D
20

If the equation below is solved by graphing, which statement is true?

Question illustration
A
The curves intersect at approximately x = 0.46.
B
The curves intersect at approximately x = 0.75.
C
The curves intersect at approximately x = 1.11.
D
The curves intersect at approximately x = 3.07.

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