AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Base e

Base e — Unit test Answers

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1
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The two expressions below have the same value when rounded to the nearest hundredth.What is the approximate value of to the nearest hundredth?

Question illustration
A
0.93
B
1.23
C
9.16
D
65.53
2
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Which of the following shows the graph of

Question illustration
A
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 0.5, 0).
Option A
B
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 4, 0).
Option B
C
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (0.5, 0).
Option C
D
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (4, 0).
Option D
3

Identify the equation that translates five units down.

Question illustration
A
y = l n (x minus 5)
Option A
B
y = l n (x) + 5
Option B
C
y = l n (x + 5)
Option C
D
y = l n (x) minus 5
Option D
4

Which function is shown in the graph below?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

What is the range of ?

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a
all real numbers not equal to 0
a
all real numbers less than 6
a
all real number greater than 6
a
all real numbers
6

Which is the graph of ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

Which expression is equivalent to ?

Question illustration
A
log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x
Option A
B
log Subscript 2 Baseline x + 3 log Subscript 2 Baseline 9
Option B
C
3 log Subscript 2 Baseline x minus log Subscript 2 Baseline 9
Option C
D
3 log Subscript 2 Baseline 9 minus log Subscript 2 Baseline x
Option D
8

What is the range of the function f(x) = –2(6x) + 3?

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

Which expression is equivalent to ?

Question illustration
A
log StartFraction 3 StartRoot x EndRoot (x cubed + 4) Over 2 EndFraction
Option A
B
log StartFraction 3 StartRoot x EndRoot (3 x + 4) Over 2 EndFraction
Option B
C
log StartFraction StartRoot 9 x (x cubed + 4) EndRoot Over 6 EndFraction
Option C
D
StartFraction StartRoot log 9 x ( x cubed + 4) EndRoot Over 6 EndFraction
Option D
10

What is written as a single logarithm?

Question illustration
A
4 log Subscript one-half Baseline 2 Superscript 4 Baseline u squared minus v cubed
Option A
B
log Subscript one-half Baseline w Superscript 4 Baseline (StartFraction u squared Over v cubed EndFraction)
Option B
C
log Subscript one-half Baseline (StartFraction w Superscript 4 Baseline Over u squared v cubed EndFraction)
Option C
D
log Subscript one-half Baseline (w (StartFraction u squared Over v cubed EndFraction)) Superscript 4
Option D
11

Jerome solved the equation below by graphing.Which of the following shows the correct system of equations and solution?

Question illustration
A
; x = 3
Option A
B
; x = 4
Option B
C
; x = 33
Option C
D
; x = 44
Option D
12

Which of the following shows the graph of y = –(2)x – 1?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
13

Which of the following shows the extraneous solution to the logarithmic equation below?

Question illustration
A
x = negative 6
Option A
B
x = negative 4
Option B
C
x = negative 2
Option C
D
x = negative 1
Option D
14

Which function has a horizontal asymptote of y = 3?

f
f(x) = 3(2x)
f
f(x) = 2(4)x–3
f
f(x) = 2(3x)
f
f(x) = 2(4x) + 3
15

A student showed the steps below while solving the equation by graphing.Step 1:Write a system of equations: Step 2: Use the change of base formula to rewrite the equations:Step 3:Graph the two equations:Step 4:Identify the x-value at the point of intersection:In which step did the student make the first error?

Question illustration
A
step 1
B
step 2
C
step 3
D
step 4

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