Unit 2.8 – 2.12 Quiz
2 Form A
3−2𝑥𝑥
1. The function 𝑓𝑓 is given by 𝑓𝑓 𝑥𝑥 = 4−2𝑥𝑥
. Find the inverse of the function.
4𝑥𝑥 − 3 4𝑥𝑥 − 2
A. 𝑓𝑓 −1 𝑥𝑥 = B. 𝑓𝑓 −1 𝑥𝑥 =
2𝑥𝑥 − 2 3𝑥𝑥 − 2
4 − 2𝑥𝑥 3𝑥𝑥 − 2
C. 𝑓𝑓 −1 𝑥𝑥 = D. 𝑓𝑓 −1 𝑥𝑥 =
3 − 2𝑥𝑥 4𝑥𝑥 − 2
2. If 𝑓𝑓 𝑥𝑥 = 2𝑥𝑥+4 − 5, what is the equation for the asymptote of 𝑓𝑓 −1 (𝑥𝑥) ?
A. 𝑥𝑥 = 4 B. 𝑦𝑦 = 5
C. 𝑦𝑦 = −4 D. 𝑥𝑥 = −5
3. Assume 𝑥𝑥, 𝑦𝑦, and 𝑧𝑧 are positive. Use properties of logarithms to write the expression as a
single logarithm.
7 ln 𝑥𝑥 + 4 ln 𝑦𝑦 − 3 ln(𝑧𝑧)
7𝑥𝑥 + 4𝑦𝑦
A. ln 7𝑥𝑥 + 4𝑦𝑦 − 3𝑧𝑧 B. ln
3𝑧𝑧
𝑥𝑥 7 𝑦𝑦 4
C. ln D. ln 𝑥𝑥 7 + 𝑦𝑦 4 − 𝑧𝑧 3
𝑧𝑧 3
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, 4. The parent function is given as 𝑓𝑓 𝑥𝑥 = log 2(𝑥𝑥) and 𝑔𝑔 𝑥𝑥 = − log 2(𝑥𝑥 − 3) is a transformation
of the parent function 𝑓𝑓. Which of the following sequences of transformations maps the graph
of 𝑓𝑓 to the graph of 𝑔𝑔 in the 𝑥𝑥𝑥𝑥 −plane?
A. Reflection of the graph of 𝑓𝑓 across the 𝑦𝑦-axis , followed by a vertical
translation of 𝑓𝑓 by 3 units down.
B. Reflection of the graph of 𝑓𝑓 across the 𝑦𝑦-axis , followed by a vertical
translation of 𝑓𝑓 by 3 units up.
C. Reflection of the graph of 𝑓𝑓 across the 𝑥𝑥-axis , followed by a horizontal
translation of 𝑓𝑓 by 3 units to the left.
Reflection of the graph of 𝑓𝑓 across the 𝑥𝑥-axis , followed by a horizontal
D.
translation of 𝑓𝑓 by 3 units to the right.
5. If 𝑓𝑓 𝑥𝑥 = 𝑥𝑥 3 − 1, then 𝑓𝑓 −1 (7) equals
A. 1 B. 2
C. 3 D. 4
6. Use the table below to determine whether the function is exponential behavior or logarithmic
behavior. Give a reason to explain your answer.
𝒙𝒙 0 1 3 7 15
𝒉𝒉(𝒙𝒙) 0 1 2 3 4
A. Exponential behavior, because input values are increasing by (2)𝑛𝑛 ,
as the output values are decreasing by one.
B. Exponential behavior, because input values are increasing by a factor of 2,
as output values are decreasing by one.
C. Logarithmic behavior, because input values are increasing by (2)𝑛𝑛 ,
as output values are increasing by one.
D. Logarithmic behavior, because input values are increasing by a factor of 2,
as output values are decreasing by one.
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2 Form A
3−2𝑥𝑥
1. The function 𝑓𝑓 is given by 𝑓𝑓 𝑥𝑥 = 4−2𝑥𝑥
. Find the inverse of the function.
4𝑥𝑥 − 3 4𝑥𝑥 − 2
A. 𝑓𝑓 −1 𝑥𝑥 = B. 𝑓𝑓 −1 𝑥𝑥 =
2𝑥𝑥 − 2 3𝑥𝑥 − 2
4 − 2𝑥𝑥 3𝑥𝑥 − 2
C. 𝑓𝑓 −1 𝑥𝑥 = D. 𝑓𝑓 −1 𝑥𝑥 =
3 − 2𝑥𝑥 4𝑥𝑥 − 2
2. If 𝑓𝑓 𝑥𝑥 = 2𝑥𝑥+4 − 5, what is the equation for the asymptote of 𝑓𝑓 −1 (𝑥𝑥) ?
A. 𝑥𝑥 = 4 B. 𝑦𝑦 = 5
C. 𝑦𝑦 = −4 D. 𝑥𝑥 = −5
3. Assume 𝑥𝑥, 𝑦𝑦, and 𝑧𝑧 are positive. Use properties of logarithms to write the expression as a
single logarithm.
7 ln 𝑥𝑥 + 4 ln 𝑦𝑦 − 3 ln(𝑧𝑧)
7𝑥𝑥 + 4𝑦𝑦
A. ln 7𝑥𝑥 + 4𝑦𝑦 − 3𝑧𝑧 B. ln
3𝑧𝑧
𝑥𝑥 7 𝑦𝑦 4
C. ln D. ln 𝑥𝑥 7 + 𝑦𝑦 4 − 𝑧𝑧 3
𝑧𝑧 3
© 2023 Jean Adams Flamingo Math.com
, 4. The parent function is given as 𝑓𝑓 𝑥𝑥 = log 2(𝑥𝑥) and 𝑔𝑔 𝑥𝑥 = − log 2(𝑥𝑥 − 3) is a transformation
of the parent function 𝑓𝑓. Which of the following sequences of transformations maps the graph
of 𝑓𝑓 to the graph of 𝑔𝑔 in the 𝑥𝑥𝑥𝑥 −plane?
A. Reflection of the graph of 𝑓𝑓 across the 𝑦𝑦-axis , followed by a vertical
translation of 𝑓𝑓 by 3 units down.
B. Reflection of the graph of 𝑓𝑓 across the 𝑦𝑦-axis , followed by a vertical
translation of 𝑓𝑓 by 3 units up.
C. Reflection of the graph of 𝑓𝑓 across the 𝑥𝑥-axis , followed by a horizontal
translation of 𝑓𝑓 by 3 units to the left.
Reflection of the graph of 𝑓𝑓 across the 𝑥𝑥-axis , followed by a horizontal
D.
translation of 𝑓𝑓 by 3 units to the right.
5. If 𝑓𝑓 𝑥𝑥 = 𝑥𝑥 3 − 1, then 𝑓𝑓 −1 (7) equals
A. 1 B. 2
C. 3 D. 4
6. Use the table below to determine whether the function is exponential behavior or logarithmic
behavior. Give a reason to explain your answer.
𝒙𝒙 0 1 3 7 15
𝒉𝒉(𝒙𝒙) 0 1 2 3 4
A. Exponential behavior, because input values are increasing by (2)𝑛𝑛 ,
as the output values are decreasing by one.
B. Exponential behavior, because input values are increasing by a factor of 2,
as output values are decreasing by one.
C. Logarithmic behavior, because input values are increasing by (2)𝑛𝑛 ,
as output values are increasing by one.
D. Logarithmic behavior, because input values are increasing by a factor of 2,
as output values are decreasing by one.
© 2023 Jean Adams Flamingo Math.com
