Unit 2 Exponential & Logarithmic Functions Mid-Unit Test Form A and B Answered 2026.
Exponential & Logarithmic
Unit
Functions Mid-Unit Test
2 Form A
1. Which statement best describes the sequence 6, 2, −2, −6, . . .?
1 1
A. Geometric; 𝑟𝑟 = 3
B. Geometric; 𝑟𝑟 = − 3
C. Arithmetic; 𝑑𝑑 = −3 D. Arithmetic; 𝑑𝑑 = −4
2. List the transformations of 𝑓𝑓 𝑥𝑥 = 3𝑥𝑥+2 − 5 .
A. Horizontal translation of 2, vertical translation of 5
B. Horizontal translation of −2, vertical translation of −5
C. Horizontal translation of 2, vertical translation of −5
D. Horizontal translation of −2, vertical translation of 5
3. Use the properties of exponents to rewrite 𝑔𝑔 𝑥𝑥 = 4𝑥𝑥+2 in the form 𝑦𝑦 = 𝑎𝑎𝑏𝑏 𝑥𝑥
A. 𝑔𝑔 𝑥𝑥 = 16 4 𝑥𝑥
B. 𝑔𝑔 𝑥𝑥 = 2 4 𝑥𝑥
1 𝑥𝑥
C. 𝑔𝑔 𝑥𝑥 = 4
4 D. 𝑔𝑔 𝑥𝑥 16𝑥𝑥
4. Find the inverse of the function:
𝑥𝑥 + 3
𝑓𝑓 𝑥𝑥 =
𝑥𝑥 − 5
𝑥𝑥 − 5 𝑥𝑥 − 3
A. 𝑓𝑓 −1 𝑥𝑥 = B. 𝑓𝑓 −1 𝑥𝑥 =
𝑥𝑥 + 3 𝑥𝑥 + 5
5𝑥𝑥 + 3 −𝑥𝑥 − 3
C. 𝑓𝑓 −1 𝑥𝑥 = D. 𝑓𝑓 −1 𝑥𝑥 =
𝑥𝑥 − 1 5 − 𝑥𝑥
© 2023 Jean Adams Flamingo Math.com
, Linear Regression Exponential Regression
Residual Plot Residual Plot
5. A linear and an exponential regression were done for the same set of data. The residual plots
for each are above. Which model is the best model and why?
A. Linear, the residual plot shows a pattern.
B. Linear, the residual plot doesn’t show a pattern.
C. Exponential, the residual plot shows a pattern.
D. Exponential, the residual plot doesn’t show a pattern.
6. A point on 𝑓𝑓(𝑥𝑥) is 4, −2 , what would be the new point on y = 3𝑓𝑓 2 𝑥𝑥 + 1 −4?
A. (1, −10) B. (3, −10)
C. (7, −10) D. (9, −10)
7. The graph at the right has a maximum at (0.214, 8.209)
and a minimum at (3.120, −4.061). Which of the following
best describes the graph on the interval (1, 2)?
A. positive and increasing
B. positive and decreasing
C. negative and increasing
D. negative and decreasing
© 2023 Jean Adams Flamingo Math.com
, Exponential & Logarithmic
Unit
Functions Mid-Unit Test
2 Form A
Calculator Not Allowed
Select values of 𝑓𝑓(𝑥𝑥) are given in the table below:
𝒙𝒙 0 1 2 3 4
𝒇𝒇(𝒙𝒙) 3 9 27 81 243
𝑔𝑔 𝑥𝑥 = 4 0.7 𝑥𝑥 .
A. (i) If the function 𝑓𝑓 best modeled by a linear or an exponential function?
(ii) Give a reason for your answer in part (i).
B. (i) Write the end behavior of 𝑔𝑔(𝑥𝑥) as 𝑥𝑥 decreases without bounds in limit notation.
(ii) Find the average rate of change of 𝑓𝑓(𝑥𝑥) on the interval [1, 2].
Select values of ℎ(𝑥𝑥) are given in the table below.
𝒙𝒙 0 1 2 3 4
𝒉𝒉(𝒙𝒙) 1 5 13 29 61
𝑥𝑥 2 − 𝑥𝑥 − 2
𝑗𝑗 𝑥𝑥 =
𝑥𝑥 + 3
C. (i) Find the constant value that can be added/subtracted to the output values to reveal a
proportional growth patter. Then write an equation to model the function.
(ii) Find the interval(s) where 𝑗𝑗 𝑥𝑥 ≤ 0.
© 2023 Jean Adams Flamingo Math.com
Exponential & Logarithmic
Unit
Functions Mid-Unit Test
2 Form A
1. Which statement best describes the sequence 6, 2, −2, −6, . . .?
1 1
A. Geometric; 𝑟𝑟 = 3
B. Geometric; 𝑟𝑟 = − 3
C. Arithmetic; 𝑑𝑑 = −3 D. Arithmetic; 𝑑𝑑 = −4
2. List the transformations of 𝑓𝑓 𝑥𝑥 = 3𝑥𝑥+2 − 5 .
A. Horizontal translation of 2, vertical translation of 5
B. Horizontal translation of −2, vertical translation of −5
C. Horizontal translation of 2, vertical translation of −5
D. Horizontal translation of −2, vertical translation of 5
3. Use the properties of exponents to rewrite 𝑔𝑔 𝑥𝑥 = 4𝑥𝑥+2 in the form 𝑦𝑦 = 𝑎𝑎𝑏𝑏 𝑥𝑥
A. 𝑔𝑔 𝑥𝑥 = 16 4 𝑥𝑥
B. 𝑔𝑔 𝑥𝑥 = 2 4 𝑥𝑥
1 𝑥𝑥
C. 𝑔𝑔 𝑥𝑥 = 4
4 D. 𝑔𝑔 𝑥𝑥 16𝑥𝑥
4. Find the inverse of the function:
𝑥𝑥 + 3
𝑓𝑓 𝑥𝑥 =
𝑥𝑥 − 5
𝑥𝑥 − 5 𝑥𝑥 − 3
A. 𝑓𝑓 −1 𝑥𝑥 = B. 𝑓𝑓 −1 𝑥𝑥 =
𝑥𝑥 + 3 𝑥𝑥 + 5
5𝑥𝑥 + 3 −𝑥𝑥 − 3
C. 𝑓𝑓 −1 𝑥𝑥 = D. 𝑓𝑓 −1 𝑥𝑥 =
𝑥𝑥 − 1 5 − 𝑥𝑥
© 2023 Jean Adams Flamingo Math.com
, Linear Regression Exponential Regression
Residual Plot Residual Plot
5. A linear and an exponential regression were done for the same set of data. The residual plots
for each are above. Which model is the best model and why?
A. Linear, the residual plot shows a pattern.
B. Linear, the residual plot doesn’t show a pattern.
C. Exponential, the residual plot shows a pattern.
D. Exponential, the residual plot doesn’t show a pattern.
6. A point on 𝑓𝑓(𝑥𝑥) is 4, −2 , what would be the new point on y = 3𝑓𝑓 2 𝑥𝑥 + 1 −4?
A. (1, −10) B. (3, −10)
C. (7, −10) D. (9, −10)
7. The graph at the right has a maximum at (0.214, 8.209)
and a minimum at (3.120, −4.061). Which of the following
best describes the graph on the interval (1, 2)?
A. positive and increasing
B. positive and decreasing
C. negative and increasing
D. negative and decreasing
© 2023 Jean Adams Flamingo Math.com
, Exponential & Logarithmic
Unit
Functions Mid-Unit Test
2 Form A
Calculator Not Allowed
Select values of 𝑓𝑓(𝑥𝑥) are given in the table below:
𝒙𝒙 0 1 2 3 4
𝒇𝒇(𝒙𝒙) 3 9 27 81 243
𝑔𝑔 𝑥𝑥 = 4 0.7 𝑥𝑥 .
A. (i) If the function 𝑓𝑓 best modeled by a linear or an exponential function?
(ii) Give a reason for your answer in part (i).
B. (i) Write the end behavior of 𝑔𝑔(𝑥𝑥) as 𝑥𝑥 decreases without bounds in limit notation.
(ii) Find the average rate of change of 𝑓𝑓(𝑥𝑥) on the interval [1, 2].
Select values of ℎ(𝑥𝑥) are given in the table below.
𝒙𝒙 0 1 2 3 4
𝒉𝒉(𝒙𝒙) 1 5 13 29 61
𝑥𝑥 2 − 𝑥𝑥 − 2
𝑗𝑗 𝑥𝑥 =
𝑥𝑥 + 3
C. (i) Find the constant value that can be added/subtracted to the output values to reveal a
proportional growth patter. Then write an equation to model the function.
(ii) Find the interval(s) where 𝑗𝑗 𝑥𝑥 ≤ 0.
© 2023 Jean Adams Flamingo Math.com
