Topic 2.1: Change in Arithmetic and Geometric Sequences
1. Values of the terms of a geometric sequence g n are graphed in the figure. Which of the following is an expression for
the nth term of the geometric sequence?
1æ1ö
(A) ç ÷
4è2ø
n
(B)
1 n
×2
2
(C) ( 2 )
(D) 4 ( 2)
n-1
n-4
2. Values of the terms of a geometric sequence g n are graphed in the figure. Which of the following is an expression for
the nth term of the geometric sequence?
æ2ö
(A) 9 ç ÷
è3ø
n
AP Style MCQ
æ2ö
(B) 6 ç ÷
è3ø
n-1
æ3ö
(C) 9 ç ÷
è2ø
Unit 2
n-1
æ2ö
(D) 4 ç ÷
è3ø
n- 3
Created by Bryan Passwater
3. Values of the terms of a geometric sequence g n are graphed in the figure. Which of the following is an expression for
the nth term of the geometric sequence?
æ1ö
÷
è2ø
n-1
(A) -4 ç
æ 1ö
è 2ø
n-1
æ1ö
è2ø
(B) 4 ç - ÷
n-1
æ 1ö
è 2ø
n
(D) 8 ç - ÷
(C) 4 ç ÷
4. Values of the terms of a geometric sequence g n are graphed in the figure. Which of the following is an expression for
the nth term of the geometric sequence?
æ1ö
÷
è2ø
n 2
(A) 5 ç
AP Style MCQ
æ1ö
è2ø
n- 2
æ1ö
è2ø
(B) 5 ç ÷
(C) 10 ç ÷
Unit 2
n 2
æ1ö
è2ø
2n
(D) 10 ç ÷
Created by Bryan Passwater
5. A large theater has rows of seats arranged in a way that the number of seats in each consecutive row form an arithmetic
sequence. If the fourth row contains 30 seats and the eighth row contains 54 seats, which of the following gives the
number of seats in the tenth row?
(A) 60
(B) 66
(C) 75
(D) 78
6. Let an represent an arithmetic sequence where a3 = 22 and a6 = 10. What is the value of a12 ?
(A) -48
(B) -14
(C) -4
(D) -2
𝑛
0
1
2
3
4
𝑠!
12
6
0
−6
−12
7. The table gives values of the sequence sn at selected values of n. Which of the following statements about sn is true?
(A) sn could be an arithmetic sequence, because successive terms have a constant difference.
(B) sn could be an arithmetic sequence, because successive terms have constant proportional change.
(C) sn could be a geometric sequence, because successive terms have a constant difference.
(D) sn could be a geometric sequence, because successive terms have constant proportional change.
𝑛
2
3
4
5
6
𝑠!
1
2
4
8
16
8. The table gives values of the sequence sn at selected values of n. Which of the following statements about sn is true?
(A) sn could be an arithmetic sequence, because successive terms have a constant difference.
(B) sn could be an arithmetic sequence, because successive terms have constant proportional change.
(C) sn could be a geometric sequence, because successive terms have a constant difference.
(D) sn could be a geometric sequence, because successive terms have constant proportional change.
AP Style MCQ
Unit 2
Created by Bryan Passwater
n
1
5
7
8
15
an
b
32
26
c
2
9. The table above contains selected values of an arithmetic sequence an , where b and c are constants. What is the value
of b + c ?
(A) 49
(B) 58
(C) 67
(D) 76
10. Let g n be a geometric sequence with g1 = 3 and g 4 = 24 . Which of the following is the value of g 3 ?
(A) 6
(B) 8
(D) 17
(C) 12
Topic 2.2: Change in Linear and Exponential Functions
11. The number of students at Speedway High School that earn a qualifying score on an AP math exam can be modeled
using an arithmetic sequence, where the Mr. Passwater’s first year at SHS is year 1. The number of students earning a
qualifying score in year 3 was 52, and the number of students earning a qualifying score in year 6 was 61. Which of
the following functions gives the number of SHS students earning a qualifying score in year t , where t is a whole
number?
1
3
(A) f ( t ) = t + 51
(B) g ( t ) = 3t + 43
(C) h ( t ) = 3t + 52
(D) k ( t ) = 3t + 61
12. (Calculator Active) Fearing a new computer virus, a security company performs a simulation to predict the number
of computers that might be affected by the virus. The number of infected computers can be modeled by a geometric
sequence, where the first day of the simulation is day 1. On day 6, the virus had infected 750 computers, and on day
10 the virus had infected 3200 computers. To the nearest whole number, how many computers had been infected by
the virus on day 14 based on the simulation?
(A) 5, 650
AP Style MCQ
(B) 5, 717
(C) 13, 653
Unit 2
(D) 120,329
Created by Bryan Passwater
Topic 2.3: Exponential Functions
x
æ2ö
13. The function f is given by f ( x ) = 4 ç ÷ . Which of the following describes the end behavior of f ?
è3ø
(A) lim f ( x ) = -¥ and lim f ( x ) = ¥
x ®-¥
x ®¥
(B) lim f ( x ) = ¥ and lim f ( x ) = -¥
x ®-¥
x ®¥
x ®-¥
x ®¥
x ®-¥
x ®¥
(C) lim f ( x ) = 0 and lim f ( x ) = ¥
(D) lim f ( x ) = ¥ and lim f ( x ) = 0
14. The function g is given by g ( x ) = 2 ( 3) . Which of the following describes the end behavior of g ?
x
(A) lim g ( x ) = 0 and lim g ( x ) = -¥
x ®-¥
x ®¥
(B) lim g ( x ) = -¥ and lim g ( x ) = 0
x ®-¥
x ®¥
(C) lim g ( x ) = 0 and lim g ( x ) = ¥
x ®-¥
x ®¥
x ®-¥
x ®¥
(D) lim g ( x ) = ¥ and lim g ( x ) = 0
2
x
( 4 ) . Which of the following describes the end behavior of h ?
5
(A) lim h ( x ) = 0 and lim h ( x ) = -¥
15. The function h is given by h ( x ) =
x ®-¥
x ®¥
(B) lim h ( x ) = -¥ and lim h ( x ) = 0
x ®-¥
x ®¥
(C) lim h ( x ) = 0 and lim h ( x ) = ¥
x ®-¥
x ®¥
x ®-¥
x ®¥
(D) lim h ( x ) = ¥ and lim h ( x ) = 0
16. The function k is given by k ( x ) = -3 ( 5) . Which of the following describes the end behavior of k ?
x
(A) lim k ( x ) = 0 and lim k ( x ) = -¥
x ®-¥
x ®¥
(B) lim k ( x ) = -¥ and lim k ( x ) = 0
x ®-¥
x ®¥
(C) lim k ( x ) = 0 and lim k ( x ) = ¥
x ®-¥
x ®¥
x ®-¥
x ®¥
(D) lim k ( x ) = ¥ and lim k ( x ) = 0
AP Style MCQ
Unit 2
Created by Bryan Passwater
æ1ö
è3ø
(A) lim j ( x ) = 0 and lim j ( x ) = -¥
x
17. The function j is given by j ( x ) = -5 ç ÷ . Which of the following describes the end behavior of j ?
x ®-¥
x ®¥
(B) lim j ( x ) = -¥ and lim j ( x ) = 0
x ®-¥
x ®¥
(C) lim j ( x ) = 0 and lim j ( x ) = ¥
x ®-¥
x ®¥
x ®-¥
x ®¥
(D) lim j ( x ) = ¥ and lim j ( x ) = 0
1 x
( 3) . Which of the following describes the end behavior of f ?
4
(A) lim f ( x ) = 0 and lim f ( x ) = -¥
18. The function f is given by f ( x ) = x ®-¥
x ®¥
(B) lim f ( x ) = -¥ and lim f ( x ) = 0
x ®-¥
x ®¥
(C) lim f ( x ) = 0 and lim f ( x ) = ¥
x ®-¥
x ®¥
x ®-¥
x ®¥
(D) lim f ( x ) = ¥ and lim f ( x ) = 0
x
æ4ö
19. The function g is given by g ( x ) = -2 ç ÷ . Which of the following describes the end behavior of g ?
è3ø
(A) lim g ( x ) = 0 and lim g ( x ) = -¥
x ®-¥
x ®¥
(B) lim g ( x ) = -¥ and lim g ( x ) = 0
x ®-¥
x ®¥
(C) lim g ( x ) = 0 and lim g ( x ) = ¥
x ®-¥
x ®¥
x ®-¥
x ®¥
(D) lim g ( x ) = ¥ and lim g ( x ) = 0
𝑥
0
1
2
3
4
𝑓(𝑥)
36
18
9
9
2
9
4
20. The exponential function f is defined by f ( x ) = ab x , where a and b are positive constants. The table gives
values of f ( x ) at selected values of x. Which of the following statements is true?
(A) f demonstrates exponential decay because a > 0 and 0 < b < 1.
(B) f demonstrates exponential decay because a > 0 and b > 1.
(C) f demonstrates exponential growth because a > 0 and 0 < b < 1.
(D) f demonstrates exponential growth because a > 0 and b > 1.
AP Style MCQ
Unit 2
Created by Bryan Passwater
𝑥
1
2
3
4
5
ℎ(𝑥)
2
6
18
54
162
21. The exponential function h is defined by h ( x ) = ab x , where a and b are positive constants. The table gives values
of h ( x ) at selected values of x. Which of the following statements is true?
(A) h demonstrates exponential decay because a > 0 and 0 < b < 1.
(B) h demonstrates exponential decay because a > 0 and b > 1.
(C) h demonstrates exponential growth because a > 0 and 0 < b < 1.
(D) h demonstrates exponential growth because a > 0 and b > 1.
𝑥
1
2
3
4
5
𝑘(𝑥)
8
12
18
27
81
2
22. The exponential function k is defined by k ( x ) = ab x , where a and b are positive constants. The table gives values
of k ( x ) at selected values of x. Which of the following statements is true?
(A) k demonstrates exponential decay because a > 0 and 0 < b < 1.
(B) k demonstrates exponential decay because a > 0 and b > 1.
(C) k demonstrates exponential growth because a > 0 and 0 < b < 1.
(D) k demonstrates exponential growth because a > 0 and b > 1.
𝑥
0
1
2
3
4
𝑓(𝑥)
54
36
24
16
32
3
23. The exponential function f is defined by f ( x ) = ab x , where a and b are positive constants. The table gives
values of f ( x ) at selected values of x. Which of the following statements is true?
(A) f demonstrates exponential decay because a > 0 and 0 < b < 1.
(B) f demonstrates exponential decay because a > 0 and b > 1.
(C) f demonstrates exponential growth because a > 0 and 0 < b < 1.
(D) f demonstrates exponential growth because a > 0 and b > 1.
AP Style MCQ
Unit 2
Created by Bryan Passwater
æ1ö
è3ø
x
24. Which of the following statements is true about the exponential function f given by f ( x ) = 4 ç ÷ ?
(A) f is always increasing, and the graph of f is always concave up.
(B) f is always increasing, and the graph of f is always concave down.
(C) f is always decreasing, and the graph of f is always concave up.
(D) f is always decreasing, and the graph of f is always concave down.
25. Which of the following statements is true about the exponential function g given by g ( x ) =
1 x
×3 ?
2
(A) g is always increasing, and the graph of g is always concave up.
(B) g is always increasing, and the graph of g is always concave down.
(C) g is always decreasing, and the graph of g is always concave up.
(D) g is always decreasing, and the graph of g is always concave down.
26. Which of the following statements is true about the exponential function h given by h ( x ) = 3 × 5x ?
(A) h is always increasing, and the graph of h is always concave up.
(B) h is always increasing, and the graph of h is always concave down.
(C) h is always decreasing, and the graph of h is always concave up.
(D) h is always decreasing, and the graph of h is always concave down.
27. Which of the following statements is true about the exponential function k given by k ( x ) = -4 × 3x ?
(A) k is always increasing, and the graph of k is always concave up.
(B) k is always increasing, and the graph of k is always concave down.
(C) k is always decreasing, and the graph of k is always concave up.
(D) k is always decreasing, and the graph of k is always concave down.
x
æ2ö
28. Which of the following statements is true about the exponential function j given by j ( x ) = -6 ç ÷ ?
è7ø
(A) j is always increasing, and the graph of j is always concave up.
(B) j is always increasing, and the graph of j is always concave down.
(C) j is always decreasing, and the graph of j is always concave up.
(D) j is always decreasing, and the graph of j is always concave down.
AP Style MCQ
Unit 2
Created by Bryan Passwater
1
3
29. Which of the following statements is true about the exponential function f given by f ( x ) = - × 2 x ?
(A) f is always increasing, and the graph of f is always concave up.
(B) f is always increasing, and the graph of f is always concave down.
(C) f is always decreasing, and the graph of f is always concave up.
(D) f is always decreasing, and the graph of f is always concave down.
x
æ4ö
30. Which of the following statements is true about the exponential function f given by f ( x ) = 7 ç ÷ ?
è5ø
(A) f is increasing at an increasing rate.
(B) f is increasing at a decreasing rate.
(C) f is decreasing at an increasing rate.
(D) f is decreasing at a decreasing rate.
31. Which of the following statements is true about the exponential function g given by g ( x ) = -6 × 5x ?
(A) g is increasing at an increasing rate.
(B) g is increasing at a decreasing rate.
(C) g is decreasing at an increasing rate.
(D) g is decreasing at a decreasing rate.
32. Which of the following statements is true about the exponential function h given by h ( x ) = 4 × 9x ?
(A) h is increasing at an increasing rate.
(B) h is increasing at a decreasing rate.
(C) h is decreasing at an increasing rate.
(D) h is decreasing at a decreasing rate.
AP Style MCQ
Unit 2
Created by Bryan Passwater
Graph of h
33. The figure shows a portion of the graph of a function h. Which of the following conclusions is possible for h ?
(A) h is logarithmic because the output values are proportional over equal-length input-value intervals.
(B) h is logarithmic because the input values are proportional over equal-length output-value intervals.
(C) h is exponential because the output values are proportional over equal-length input-value intervals.
(D) h is exponential because the input values are proportional over equal-length output-value intervals.
Graph of g
34. The figure shows a portion of the graph of a function g . Which of the following conclusions is possible for g ?
(A) g is logarithmic because the output values are proportional over equal-length input-value intervals.
(B) g is logarithmic because the input values are proportional over equal-length output-value intervals.
(C) g is exponential because the output values are proportional over equal-length input-value intervals.
(D) g is exponential because the input values are proportional over equal-length output-value intervals.
AP Style MCQ
Unit 2
Created by Bryan Passwater
Graph of f
35. The figure shows a portion of the graph of a function f . Which of the following conclusions is possible for f ?
(A) f is quadratic because the output values are proportional over equal-length input-value intervals.
(B) f is quadratic because the average rates of change over consecutive equal-length input-value intervals can be
given by a linear function.
(C) f is exponential because the output values are proportional over equal-length input-value intervals.
(D) f is exponential because the average rates of change over consecutive equal-length input-value intervals can be
given by a linear function.
Topic 2.4: Exponential Function Manipulation
36. The function f is given by f ( x ) = 36 × 4 x. Which of the following is an equivalent form for f ( x ) ?
(A) f ( x ) = 6 × 2( x 2)
(B) f ( x ) = 6 × 2( 2 x )
(C) f ( x ) = 36 × 2( x 2)
(D) f ( x ) = 36 × 2( 2 x )
37. The function j is given by j ( x ) = 3 × 4( x + 2). Which of the following is an equivalent form for j ( x ) ?
(A) j ( x ) = 48x
(B) j ( x ) = 48 × 4 x
(C) j ( x ) = 3 ×16x
(D) j ( x ) = 9 ×16x
AP Style MCQ
Unit 2
Created by Bryan Passwater
38. Which of the following functions is an equivalent form of the function g ( x ) = 3 × 52 x ?
(A) g ( x ) = 75x
(B) g ( x ) = 3 × 25x
(C) g ( x ) = 9 × 5x
(D) g ( x ) = 9 × 25x
39. The function h is given by h ( x ) = 25 ×16( x 2) . Which of the following is an equivalent form for h ( x ) ?
(A) h ( x ) = 100x
(B) h ( x ) = 5 × 4x
(C) h ( x ) = 25 × 4 x
(D) h ( x ) = 25 × 8x
40. Which of the following functions is an equivalent form of the function p ( x ) = 4( -2 x ) ?
(A) p ( x ) = - (16)
(B) p ( x ) = ( 2)
x
x
æ1ö
è2ø
(C) p ( x ) = ç ÷
x
æ 1 ö
(D) p ( x ) = ç ÷
è 16 ø
x
41. In the xy -plane, the function f , given by f ( x ) = 4( x -2) , is a horizontal translation of the exponential function g ,
given by g ( x ) = 4x. Which of the following is an equivalent form for f ( x ) that expresses f as a vertical dilation
of g ?
(A) f ( x ) = -2 × 4 x
(B) f ( x ) = 16 × 4x
1 x
×4
16
1
(D) f ( x ) =
+ 4x
16
(C) f ( x ) =
AP Style MCQ
Unit 2
Created by Bryan Passwater
42. In the xy -plane, the function h, given by h ( x ) = 9 × 3x , is a vertical dilation of the exponential function k , given by
k ( x ) = 3x. Which of the following is an equivalent form for h ( x ) that expresses h as a horizontal translation of k ?
(A) h ( x ) = 3( 2 x )
(B) h ( x ) = 3( x + 2)
(C) h ( x ) = 3( x - 2)
(D) h ( x ) = 9 + 3x
43. The graph of a function f is a horizontal dilation of y = 3x , and f ( x ) is equivalent to
( 3 ) . Which of the
x
following could be an expression for f ( x ) ?
x2
(A) 3( )
2x
(B) 3( )
x2
(C) 9( )
2x
(D) 9( )
Topic 2.5: Exponential Function Context and Data Modeling
t
0
1
2
3
4
C (t )
10
30
90
270
810
44. The increasing function C gives the number of cars that are stuck in traffic due to lane closures. The table gives
values of C ( t ) for selected values of t , in minutes, since the beginning of the lane closures. If a model is
constructed to represent these data, which of the following best applies to this situation?
(A) y = 30t + 10
æ1ö
(C) y = 10 ç ÷
è3ø
(B) y = 300t + 10
t
(D) y = 10 ( 3)
t
45. The number of cars that travel along a busy highway on a particular morning can be modeled by a function C. For
0 £ t £ 8 hours, the total number of cars that have traveled on the highway at time t hours increases by 15% each
hour. At time t = 0 hours, a total of 54 cars had traveled on the highway. If t is measured in minutes, which of the
following is an expression for C ( t ) ? (Note: There are 60 minutes in one hour).
(t 60)
(A) 54 ( 0.15)
AP Style MCQ
( 60t )
(t 60)
(B) 54 ( 0.15)
(C) 54 (1.15)
Unit 2
( 60t )
(D) 54 (1.15)
Created by Bryan Passwater
46. Radon-222 has a half-life of 3.8 days. In a particular sample, the amount of Radon-222 remaining after 𝑑 days can
( d 3.8)
be modeled by the function R given by R ( d ) = A0 ( 0.5)
, where A0 is the amount of Radon-222 in the sample
at time d = 0. Which of the following functions L models the amount of Radon-222 remaining after w weeks,
where A0 is the amount of Radon-222 in the sample at time w = 0 ? (There are 7 days in a week, so d = 7 w .)
( w 7)
(A) L ( w) = A0 ( 0.5)
( )
(
)
(C) L ( w) = A ( 0.5( ) )
(
)
(D) L ( w) = A ( 0.5( ) )
3.8 w)
17 (
(B) L ( w) = A0 0.5( )
17
w 3.8
0
7
w 3.8
0
47. From 2015 – 2024, the number of residents in a small town that subscribed to the local newspaper decreased with
exponential decay. The number of residents that subscribed to the newspaper is modeled by the function S , which
decreased by 43% each year. In 2015 ( t = 0 ) , 5200 residents subscribed to the newspaper. If t is measured in
months, which of the following is an expression for S ( t ) ? (Note: There are twelve months in one year.)
(t 12)
(A) 5200 ( 0.43)
(12t )
(t 12)
(B) 5200 ( 0.43)
(C) 5200 ( 0.57 )
(12t )
(D) 5200 ( 0.57 )
48. The value, in thousands of dollars, of an investment is modeled by the function I . The value is expected to increase
by 2.9% each month of the year. At time t = 0 years, the investment had a value of 215 thousand dollars. If t is
measured in years, which of the following is an expression for M ( t ) ? (Note: A month is one twelfth of a year.)
(t 12)
(A) 215 (.029)
(12t )
(t 12)
(B) 215 (.029)
(C) 215 (1.029)
x
0
1
2
3
4
f ( x)
324
108
36
12
4
(12t )
(D) 215 (1.029)
49. The table gives values of a decreasing function f for selected values of x. If a model is constructed to represent
these data, which of the following best applies to this situation?
(A) y = -80 x + 324
AP Style MCQ
æ1ö
(C) y = 324 ç ÷
è3ø
(B) y = -216 x + 324
Unit 2
x
(D) y = 324 ( 3)
x
Created by Bryan Passwater
Topic 2.6: Competing Function Model Validation
50. A linear regression was used to create a model for a set of data. The figure shows a graph of the residuals of the linear
regression. Which of the following statements about the linear regression is true?
(A) A linear regression model is appropriate, because the residuals show a clear pattern.
(B) A linear regression model is appropriate, but a quadratic regression may be a better model.
(C) A linear regression model is not appropriate, because the residuals do not show a linear pattern.
(D) A linear regression model is not appropriate, because the residuals show a clear pattern.
51. A regression model was created for the data in the graph above (left). The residual plot for the model is given above
(right). Which of the following statements about the regression model is best?
(A) A quadratic regression model was used and the model is appropriate.
(B) A quadratic regression model was used and the model is not appropriate.
(C) An exponential regression model was used and the model is appropriate.
(D) An exponential regression model was used and the model is not appropriate.
AP Style MCQ
Unit 2
Created by Bryan Passwater
52. Mr. Passwater believed a set of data displayed exponential growth. He used the set of data to create an exponential
regression model. The residual plot for his model is shown above. Based on the residual plot above, which of the
following conclusions is correct?
(A) The residual plot has no apparent pattern, so the exponential model was appropriate.
(B) The residual plot has no apparent pattern, so the exponential model was not appropriate.
(C) The residual plot displays a pattern, so the exponential model was appropriate.
(D) The residual plot displays a pattern, so the exponential model was not appropriate.
53. A set of data was used to create a linear, a quadratic, and an exponential regression model. The residual plots for the
three models are shown above. Based on the three residual plots, which of the following could be an appropriate
model for the data?
(A) y = 3x + 1
(C) y = 4 ( 3)
(B) y = x 2 - 3x + 1
x
(D) y = 1 + log3 x
54. A set of data and the linear regression model constructed for the data set are shown in the figure, along with data point
P. Which of the following is the best estimate of the residual for data point P ?
(A) -0.5
AP Style MCQ
(B) 0.5
(C) 1.5
Unit 2
(D) 3
Created by Bryan Passwater
55. An exponential regression model S is constructed for a data set. The model S is given by S ( x ) = 3 ( 2) . The
x
coordinates of a point P from the data set are ( -1,1) . Which of the following statements is true about the residual of
point P ?
(A) The residual of point P is a negative value because the model produces an overestimate at point P.
(B) The residual of point P is a negative value because the model produces an underestimate at point P.
(C) The residual of point P is a positive value because the model produces an overestimate at point P.
(D) The residual of point P is a positive value because the model produces an underestimate at point P.
56. The figure shows a data set and its linear regression model in the xy -plane. The points P and Q are labeled. Which
of the following statements is true about the model and the estimates produced by the model that correspond to
P and Q ?
(A) The residuals for P and Q have the same sign. Based on the absolute value of the residuals, there is a greater
error in the model with P than with Q.
(B) The residuals for P and Q have the same sign. Based on the absolute value of the residuals, there is a greater
error in the model with Q than with P.
(C) The residuals for P and Q have opposite signs. Based on the absolute value of the residuals, there is a greater
error in the model with P than with Q.
(D) The residuals for P and Q have opposite signs. Based on the absolute value of the residuals, there is a greater
error in the model with Q than with P.
AP Style MCQ
Unit 2
Created by Bryan Passwater
Topic 2.7: Composition of Functions
Directions: Use the table below for problems 57 – 58.
𝑥
2
3
5
9
𝑓(𝑥)
7
2
8
5
𝑔(𝑥)
3
5
4
2
The table gives values for the functions 𝑓 and 𝑔 at selected values of 𝑥. Functions 𝑓 and 𝑔 are defined for all real
numbers.
(
)
57. Let h be the function defined by h ( x ) = g f ( x ) . What is the value of h ( 9 ) ?
(A) 4
(B) 7
(C) 8
(
(D) 10
)
58. Let k be the function defined by k ( x ) = f g ( x ) . What is the value of k ( 3) ?
(A) 3
(B) 7
(C) 8
(D) 10
Directions: Use the graphs below for problems 59 – 60.
Graph of f
Graph of g
The graphs of f and g are shown for 0 £ x £ 9, each consisting of three line segments.
(
)
59. Let h be the function defined by h ( x ) = g f ( x ) . What is the value of h (8) ?
(A) -2
(B) -1
(C) 0
(
(D) 2
)
60. Let k be the function defined by k ( x ) = f g ( x ) . What is the value of k ( 9 ) ?
(A) -3
AP Style MCQ
(B) -2
(C) 0
Unit 2
(D) 4
Created by Bryan Passwater
𝑥
1
2
3
4
5
𝑓(𝑥)
1
2
1
4
54
162
61. The table gives values of the function f for selected values of x. The function g is given by g ( x ) = 9x - 8x. What
(
)
is the value of g f (1) ?
(A) -1
(B)
1
2
(C)
3
2
(D) 65
62. The function f is given by f ( x ) = 4x , and the function g is given by g ( x ) = 3x. Which of the following is an
2
(
)
expression for f g ( x ) ?
(A) 43 x
2
(B) 46 x
2
(C) 49 x
2
(D) 3 × 4 x
2
63. The function f is given by f ( x ) = 2 x - 1, and the function g is given by g ( x ) = x 2 + 3x. Which of the following
(
)
is an expression for g f ( x ) ?
(A) 2 x + 6 x - 1
2
(B) 4 x 2 - x - 1
(C) 4 x 2 + 2 x - 2
(D) 2 x3 + 5 x 2 - 3x
AP Style MCQ
Unit 2
Created by Bryan Passwater
Topic 2.8: Inverse Functions
Graph of f
64. The graph of the piecewise defined function 𝑓 is shown above and consists of two line segments. The function g is
the inverse of 𝑓, that is g = f -1 . Which of the following is the graph of g , the inverse of f ?
(A)
(B)
(C)
(D)
AP Style MCQ
Unit 2
Created by Bryan Passwater
Graph of f
65. The graph of the piecewise defined function 𝑓 is shown above and consists of two line segments. The function g is
the inverse of 𝑓, that is g = f -1 . What is the domain of g ?
(A) [ -5, 4]
(B) [ -4, 5]
(C) [ -2, 3]
é 1 1ù
ë
û
(D) ê - , ú
4 5
Graph of h
66. The graph of the piecewise defined function ℎ is shown above and consists of two line segments. The function k is
the inverse of ℎ, that is k = h -1 . What is the minimum value of k ?
(A) -4
AP Style MCQ
(B) -3
(C) -
1
4
Unit 2
(D) -
1
3
Created by Bryan Passwater
𝑥
−4
1
4
0
4
6
𝑓(𝑥)
−5
−2
1
3
4
67. The table gives values of the increasing function f for selected values of x. What is the value of f -1 ( 4 ) ?
(B) -2
(A) -5
(C) 3
(D) 6
Directions: Use the table below for questions 68 – 70.
𝑥
1
2
4
7
𝑓(𝑥)
4
7
1
5
𝑔(𝑥)
3
4
7
2
The table gives values for the invertible functions f and g at selected values of x.
(
)
68. What is the value of f -1 g ( 4 ) ?
(B) 3
(A) 2
(
(C) 5
(D) 7
(C) 5
(D) 7
(C) 5
(D) 7
(C) 4
(D) 5
)
69. What is the value of g -1 f ( 2 ) ?
(A) 2
(B) 4
(
)
70. What is the value of g -1 f -1 ( 7 ) ?
(A) 1
(B) 4
(
)
71. What is the value of f g -1 ( 2) ?
(A) 1
(B) 2
72. The function h is increasing for all values of x, and the graph of h is concave up for all values of x. Let the
function k be the inverse of h. Which of the following statements about k is true?
(A) k is increasing, and the graph of k is concave up.
(B) k is increasing, and the graph of k is concave down.
(C) k is decreasing, and the graph of k is concave up.
(D) k is decreasing, and the graph of k is concave down.
AP Style MCQ
Unit 2
Created by Bryan Passwater
Graph of f
73. The graph of the piecewise defined function 𝑓 is shown above and consists of three line segments. What is the value
of f -1 ( 3) ?
(A) -4
(B) -2
(C) 2
(D) 4
74. The graph of h is a transformation of the function g , where h ( x ) = 2 g ( x ) + 3. If the point ( 3, - 2 ) is on the graph
of g , which of the following points is on the graph of h -1 , the inverse of h ?
(A) ( -1, 3)
(B) (1, 6 )
75. The rational function f is given by f ( x ) =
inverse of f ( x ) ?
(A)
x+4
2x - 3
(B)
2x + 3
x-4
(C) ( 2, 3)
(D) ( 3, - 1)
2x - 3
. Which of the following gives an expression for f -1 ( x ) , the
x+4
(C)
-4 x - 3
x-2
(D)
-7
x-2
76. The function g is given by g ( x ) = log3 ( x - 4 ) . Which of the following statements about the construction of the
inverse of g is true?
(A) The inverse of g cannot be constructed because the graph of g is not defined for all real values of x.
(B) The inverse of g can be constructed, and the graph of g -1 has domain of real values of x.
(C) The inverse of g can be constructed, and the graph of g -1 has domain x > 4.
(D) The inverse of g can be constructed, and the graph of g -1 has range of real values of y.
AP Style MCQ
Unit 2
Created by Bryan Passwater
Topic 2.9: Logarithmic Expressions
77. The function f is given by f ( x ) = log8 x. What is the value of f ( 2 ) ?
(A) -3
(B)
1
4
(C)
1
3
(D) 3
æ1ö
è9ø
78. The function g is given by g ( x ) = log3 x. What is the value of g ç ÷ ?
(A) -2
(B) -
1
2
(C)
1
2
(D) 2
79. The function h is given by h ( x ) = log 4 x. What input value in the domain of h yields an output value of
(A) -2
(B) -
1
2
(C)
1
2
1
?
2
(D) 2
80. The function p is given by p ( x ) = log10 x, and the function r is given by r ( x ) = 1. For which values of x will
the graphs of p and r intersect?
(A) 0
(B)
1
10
(C) 1
(D) 10
Topic 2.10: Inverses of Exponential Functions
81. The function g is given by g ( x ) = log 4 x. Which of the following statements about the inverse of g is true?
(A) The inverse of g is given by g -1 ( x ) = x 4 and is defined for all real values of x.
(B) The inverse of g is given by g -1 ( x ) = 4 x and is defined only for x > 4.
(C) The inverse of g is given by g -1 ( x ) = 4 x and is defined for all real values of x.
(D) g does not have an inverse because the graph of g is undefined for x £ 0.
AP Style MCQ
Unit 2
Created by Bryan Passwater
æ
è
82. The points ç -3,
1ö
x
÷ and ( 4, 16 ) are on the graph of the exponential function h given by h ( x ) = b , where b > 1.
8ø
Which of the following statements about the graph of k ( x ) = logb x is true?
1ö
æ
-1
÷ and ( 4, 16 ) are both on the graph of k because k = h .
8ø
è
æ1
ö
(B) The points ç , - 3 ÷ and (16, 4 ) are both on the graph of k because k = h -1.
è8
ø
æ 1 ö
æ1 1 ö
-1
(C) The points ç - , 8 ÷ and ç ,
÷ are both on the graph of k because k = h .
è 3 ø
è 4 16 ø
æ1
ö
(D) The point (16, 4 ) is on the graph of k but the point ç , - 3 ÷ is not on the graph of k because the domain of
è8
ø
h is restricted to x > 0, thus the range of k is restricted to y > 0.
(A) The points ç -3,
𝑥
80
40
20
10
5
𝑓(𝑥)
2
4
6
8
10
83. The table shows values for a function f at selected values of x. Which of the following claim and explanation
statements best fits these data?
(A) f is best modeled by an exponential function, because the input values change proportionately as output values
increase in equal-length intervals.
(B) f is best modeled by an exponential function, because the output values change proportionately as input values
increase in equal-length intervals.
(C) f is best modeled by a logarithmic function, because the input values change proportionately as output values
increase in equal-length intervals.
(D) f is best modeled by a logarithmic function, because the output values change proportionately as input values
increase in equal-length intervals.
𝑥
8
12
18
27
81
2
ℎ(𝑥)
1
2
3
4
5
84. The table shows values for a function h at selected values of x. Which of the following claim and explanation
statements best fits these data?
(A) h is best modeled by an exponential function, because the input values change proportionately as output values
increase in equal-length intervals.
(B) h is best modeled by an exponential function, because the output values change proportionately as input values
increase in equal-length intervals.
(C) h is best modeled by a logarithmic function, because the input values change proportionately as output values
increase in equal-length intervals.
(D) h is best modeled by a logarithmic function, because the output values change proportionately as input values
increase in equal-length intervals.
AP Style MCQ
Unit 2
Created by Bryan Passwater
𝑥
𝑘(𝑥)
10
2
9
20
2
3
30
40
50
2
6
18
85. The table shows values for a function k at selected values of x. Which of the following claim and explanation
statements best fits these data?
(A) k is best modeled by an exponential function, because the input values change proportionately as output values
increase in equal-length intervals.
(B) k is best modeled by an exponential function, because the output values change proportionately as input values
increase in equal-length intervals.
(C) k is best modeled by a logarithmic function, because the input values change proportionately as output values
increase in equal-length intervals.
(D) k is best modeled by a logarithmic function, because the output values change proportionately as input values
increase in equal-length intervals.
Topic 2.11: Logarithmic Functions
86. Let f be the logarithmic function given by f ( x ) = 3log10 x. Which of the following statements about f is true?
(A) f is increasing, and the graph of f is concave up.
(B) f is increasing, and the graph of f is concave down.
(C) f is decreasing, and the graph of f is concave up.
(D) f is decreasing, and the graph of f is concave down.
87. Let g be the logarithmic function given by g ( x ) = -2log3 x. Which of the following statements about g is true?
(A) g is increasing, and the graph of g is concave up.
(B) g is increasing, and the graph of g is concave down.
(C) g is decreasing, and the graph of g is concave up.
(D) g is decreasing, and the graph of g is concave down.
88. Let h be the logarithmic function given by h ( x ) = 3 - 2log 6 x. Which of the following statements about h is true?
(A) h is increasing, and the graph of h is concave up.
(B) h is increasing, and the graph of h is concave down.
(C) h is decreasing, and the graph of h is concave up.
(D) h is decreasing, and the graph of h is concave down.
AP Style MCQ
Unit 2
Created by Bryan Passwater
89. Let k be the logarithmic function given by k ( x ) =
graph of k is true?
(A) lim k ( x ) = 0
x ®¥
1
log10 x. Which of the following limit statements about the
4
(B) lim k ( x ) = ¥
(C) lim k ( x ) = -¥
x ®¥
x ®¥
(D) lim+ k ( x ) = ¥
x ®0
90. Let p be the logarithmic function given by p ( x ) = -3log 2 x. Which of the following limit statements about the
graph of p is true?
(A) lim p ( x ) = 0
x ®¥
(B) lim p ( x ) = ¥
(C) lim k ( x ) = -¥
x ®¥
x ®¥
(D) lim+ k ( x ) = -¥
x ®0
91. Let f be the logarithmic function given by f ( x ) = 5 - 4log 7 x. Which of the following statements about the end
behavior of f is true?
(A) As the input values of f increase without bound, the output values increase without bound.
(B) As the input values of f increase without bound, the output values get arbitrarily close to 0.
(C) As the input values of f decrease arbitrarily close to 0, the output values decrease without bound.
(D) As the input values of f decrease arbitrarily close to 0, the output values increase without bound.
92. Let g be the logarithmic function given by g ( x ) = 3log 2 x. Which of the following statements about the end
behavior of g is true?
(A) As the input values of g increase without bound, the output values decrease without bound.
(B) As the input values of g increase without bound, the output values get arbitrarily close to 0.
(C) As the input values of g decrease arbitrarily close to 0, the output values decrease without bound.
(D) As the input values of g decrease arbitrarily close to 0, the output values increase without bound.
AP Style MCQ
Unit 2
Created by Bryan Passwater
93. Let h be a function such that the output values of h increase without bound as the input values increase without
bound, and the output values of h decrease without bound as the input values decrease arbitrarily close to 0. Which
of the following could be the graph of h ?
(A)
(B)
(C)
(D)
Topic 2.12: Logarithmic Function Manipulation
( )
94. Which of the following expressions is equivalent to ln 4 x3 ?
(A) 4 + ln 3 + ln x
(B) 3 ( ln 4 + ln x )
(C) ln 4 + 3ln x
(D) ln 4 + ln 3 × ln x
AP Style MCQ
Unit 2
Created by Bryan Passwater
95. Let x be a positive constant. Which of the following is equivalent to log10 x - 2log10 ( x + 1) ?
æ
ö
÷
ç ( x + 1)2 ÷
è
ø
æ
x ö
(B) log10 ç
ç 2 ( x + 1) ÷÷
è
ø
x
(A) log10 ç
(
(C) log10 x ( x + 1)
æ
2
)
ö
÷
ç ( x + 1) ÷
è
ø
x
(D) log10 ç
æ 5 y2 ö
, where y and z are positive constants?
3 ÷
è z ø
96. Which of the following expressions is equivalent to log 2 ç
(A) log 2 5 + log 2 ( 2 y ) - log 2 ( 3z )
(B) 5 + 2log 2 y - 3log 2 z
(C) log 2 5 + 2log 2 y - 3log 2 z
(D)
( log 2 5) × ( 2 log 2 y )
3log 2 z
æ 2e4 ö
, where x is a positive constant?
3 ÷
è x ø
97. Which of the following expressions is equivalent to ln ç
(A) 4 + ln 2 - 3ln x
(B) 4 + ln 2 + 3ln x
(C) 4 ln 2 - 3ln x
(D) ln 2 + ln 4 - 3ln x
98. Which of the following is equivalent to 2log x - 3log y , where x and y are positive constants?
(
(A) log x - y
2
3
)
(
2
(B) log x y
3
)
æ x2 ö
(C) log ç 3 ÷
èy ø
æ 2x ö
÷
è 3y ø
(D) log ç
99. Which of the following expressions is equivalent to log7 x , where x is a positive constant?
(A) 7 log x
AP Style MCQ
(B)
log 7
log x
(C)
log x
log 7
Unit 2
(D) log x - log 7
Created by Bryan Passwater
100. Which of the following expressions is equivalent to log 4 9 ?
(A) ln 9 - ln 4
(B)
log 9 10
log 4 10
(C)
log10 4
log10 9
(D)
ln 9
ln 4
101. Let f ( x ) = ln x . Which of the following is equivalent to 2 × f ( w) - f ( z ) , where w and z are positive constants?
(
(A) ln w × z
2
)
æ w2 ö
(B) ln ç
÷
è z ø
æ 2w ö
÷
è z ø
(C) ln ç
(
(D) ln w2 - z
)
102. Let f ( x ) = log 2 ( x ) and let g ( x ) = log 2 ( 6 x ) . Which of the following statements about the graphs of f and g is
true?
(A) The graph of g is a horizontal translation of the graph of f by - log 2 6 units.
(B) The graph of g is a horizontal dilation of the graph of f by a factor of 6 .
(C) The graph of g is a vertical translation of the graph of f by log 2 6 units.
(D) The graph of g is a vertical dilation of the graph of f by a factor of 6 .
æ xö
è2ø
103. Let h ( x ) = ln ( x ) and let k ( x ) = ln ç ÷ . Which of the following statements about the graphs of h and k is
correct?
1
.
2
1
(B) The graph of h is a horizontal dilation of the graph of k by a factor of .
2
(C) The graph of k is a vertical translation of the graph of h by -2 units.
(D) The graph of h is a vertical translation of the graph of k by -2 units.
(A) The graph of k is a horizontal dilation of the graph of h by a factor of
æ 8 x3 ö
104. Let x and y be positive constants. Which of the following is equivalent to log 2 ç
?
ç y ÷÷
è
ø
æ1 ö
(A) log 2 8 + log 2 ( 3x ) - log 2 ç y ÷
è2 ø
1
(B) 3 + 3log 2 x - log 2 y
2
(C) 3 + 3log 2 x - 2log 2 y
1
(D) 8 + 3log 2 x - log 2 y
2
AP Style MCQ
Unit 2
Created by Bryan Passwater
105. Let w, y, and z be positive constants. Which of the following is equivalent to 2ln w - ln y - 3ln z ?
æ 2w ö
÷
è y × 3z ø
(A) ln ç
æ w2 ö
3 ÷
è y×z ø
(B) ln ç
æ w2 × z 3 ö
(C) ln ç
÷
è y ø
(
(D) ln w2 × y × z 3
)
Topic 2.13: Exponential and Logarithmic Equations and Inequalities
106. Consider the functions f and g given by f ( x ) = log10 ( x + 3) - log10 ( x ) and g ( x ) = 1. In the xy -plane, what
is the x-coordinate of the point of intersection of the graphs of f and g ?
(A) -
10
3
(B)
1
3
(C) 2
(D) 3
107. Consider the functions f and g given by f ( x ) = ln ( 2 x + 1) and g ( x ) = 2ln 3. In the xy -plane, what is the
x-coordinate of the point of intersection of the graphs of f and g ?
5
7
(A) -5
(B)
(C)
2
2
(D) 4
108. Consider the functions f and g given by f ( x ) = log 2 ( 3x - 1) - log 2 ( x + 1) and g ( x ) = log 2 ( 2 ) . In the
xy -plane, what is the x-coordinate of the point of intersection of the graphs of f and g ?
(A) -5
(B) 2
(C) 3
(D) there is no such value of x
109. Consider the functions f and g given by f ( x ) = log3 x - log3 4 and g ( x ) = 2. In the xy -plane, what is the
x-coordinate of the point of intersection of the graphs of f and g ?
9
(A)
(B) 8
(C) 32
4
(D) 36
110. Consider the functions f and g given by f ( x ) = log10 ( x + 3) + log10 ( x - 5) and g ( x ) = log10 ( 3x - 1) . In the
xy -plane, what are all x-coordinates of the points of intersection of the graphs of f and g ?
(A) -2 and 7
(B) -2 only
(C) 2 only
(D) 7 only
AP Style MCQ
Unit 2
Created by Bryan Passwater
(
)
111. Consider the functions f and g given by f ( x ) = ln ( 2 x + 3) + ln ( x - 1) and g ( x ) = ln x2 + 6 x - 9 . In the
xy -plane, what are all of the points of intersection of the graphs of f and g ?
(A) 2 and 3
(C) 6 and - 1
(B) 6 only
(D)
-3 + 53
2
( )
112. What are all values of x for which log2 x2 - log2 4 = 3?
(A) x = - 2 and x = 2
(B) x = - 7 and x = 7
(C) x = -2 3 and x = 2 3
(D) x = -4 2 and x = 4 2
113. What are all values of x for which ln ( 3x ) + ln 2 = 4?
(A) x =
2
3
(B) x =
e4
6
(C) x =
2e 4
3
(D) x =
e4 - 2
3
114. What are all values of x for which log7 ( x - 1) + 2 = log7 ( 4 x + 6 ) ?
(A) x = -
5
3
(B) x = -4
(C) x =
11
9
(D) there are no such values of x
(C) x =
3
2
(D) x = 6
115. What are all values of x for which 42 x +6 = 23 x ?
(A) x = -12
(B) x = -6
116. Consider the functions h and k given by h ( x ) = 9(
3 x -1)
and k ( x ) = 81( x +3). In the xy -plane, what is the
x-coordinate of the point of intersection of the graphs of h and k ?
6
14
(A) (B)
(C) 1
13
3
AP Style MCQ
Unit 2
(D) 7
Created by Bryan Passwater
( x -2 x) and p x = æ 1 ö
117. Consider the functions m and p given by m ( x ) = 4
2
( )
ç ÷
è 16 ø
x-2
. In the xy -plane, what are all
x-coordinates of the points of intersection of the graphs of m and p ?
(A) 2 only
(B) 2 and - 2
(C) 2 and -
1
2
(D) 2 and 1
118. Consider the functions h and k given by h ( x ) = 3x and k ( x ) = 9x -1. In the xy -plane, what is the x-coordinate
of the point of intersection of the graphs of h and k ?
(A) -1
(B) 0
(C) 1
(D) 2
æ1ö
è2ø
x-coordinate of the point of intersection of the graphs of g and h ?
(A) -6
(B) -2
(C) -1
119. Consider the functions g and h given by g ( x ) = 4x and h ( x ) = ç ÷
x +3
. In the xy -plane, what is the
(D) 3
120. The function f is given by f ( x ) = 3 + 2e- x . For which of the following values of x is f ( x ) = 11?
(A) x = 1 + ln 4
(B) x =
- ln 8
2
(C) x = - ln 4
(D) x =
3 - ln11
2
121. The function g is given by g ( x ) = 3x +1. For which of the following values of x is g ( x ) = 27?
(A) x = -
2
3
(B) x = 2
(C) x = 3
(D) x = 4
1
?
16
5
(D) x =
3
122. The function h is given by h ( x ) = 23 x -1. For which of the following values of x is h ( x ) =
(A) x = -4
AP Style MCQ
(B) x = -1
(C) x =
Unit 2
1
4
Created by Bryan Passwater
123. The function k is given by k ( x ) = 3 × 8x. For which of the following values of x is k ( x ) = 12?
(A) x = -
2
3
(B) x = 0
(C) x =
1
2
2
3
(D) x =
124. Consider the functions g and h given by g ( x ) = 4x +1 and h ( x ) = 23 x. Let f be the function given by
f ( x) =
(A)
g ( x)
. In the xy -plane, what is the x-coordinate of the point where f ( x ) = 1?
h ( x)
1
5
(B)
1
2
(C) 1
(D) 2
125. Consider the functions f and g given by f ( x ) = 9x -1 and g ( x ) = log3 x. Let h be the function given by
h ( x ) = g ( f ( x ) ) . In the xy -plane, on which intervals is h ( x ) > 3?
æ3 ö
è2 ø
æ5 ö
(B) ç , ¥ ÷ only
è2 ø
(A) ç , ¥ ÷
(C) ( 4, ¥ ) only
(D) ( 27, ¥ ) only
Topic 2.14: Logarithmic Function Context and Data Modeling
𝑥
(years)
𝑦
(in thousands)
1
2
4
4.5
6
107
165
248
270
307
126. The table gives the population 𝑦, in thousands, of fish in a large lake for selected times 𝑥, in years. A logarithmic
regression is used to model these data. What is the population, to the nearest thousand, predicted by the logarithmic
function model at time 5 years?
(A) 279
AP Style MCQ
(B) 280
(C) 281
Unit 2
(D) 283
Created by Bryan Passwater
𝑥
8
12
18
27
40.5
𝑓(𝑥)
2
5
8
11
14
127. The table gives values of a function 𝑓 for selected values of 𝑥. Which of the following statements about 𝑓 is most
appropriate?
(A) The function 𝑓 is best modeled by an exponential model, because the input values change proportionally over
equal-length output-value intervals.
(B) The function 𝑓 is best modeled by a logarithmic model, because the input values change proportionally over
equal-length output-value intervals.
(C) The function 𝑓 is best modeled by an exponential model, because the output values change proportionally over
equal-length input-value intervals.
(D) The function 𝑓 is best modeled by a logarithmic model, because the output values change proportionally over
equal-length input-value intervals.
128. Let g be the function defined by g ( x ) = log3 x. In the xy -plane , the graph of h is constructed by applying two
transformations to the graph of g in this order: a horizontal dilation by a factor of 2 and a vertical translation by 5
units. Which of the following defines h in terms of g ?
æ1 ö
x÷-5
è2 ø
æ1 ö
(B) h ( x ) = g ç x ÷ + 5
è2 ø
(C) h ( x ) = g ( 2 x ) + 5
(A) h ( x ) = g ç
(D) h ( x ) = g ( x - 2 ) + 5
129. For 0 £ t £ 5 minutes, shoppers enter a large mall at a rate defined by E ( t ) = 2 + 2log 6 ( t + 1) . During the same
time interval, shoppers leave the mall at a rate defined by L ( t ) = x2 - 4 x + 5, where E and L are both measured in
people per minute. What are all intervals where the rate shoppers enter the mall is greater than the rate that shoppers
leave the mall?
(A) ( 0, 0.730 ) and ( 3.648, 5 )
(B) ( 0, 2.612 ) and ( 3.715, 5)
(C) ( 0.730, 3.648)
(D) ( 2.612, 3.715)
AP Style MCQ
Unit 2
Created by Bryan Passwater
130. Let f be a function with the property that for each time the input values increase by 1, the output values double. If
the function g is the inverse of f , that is g ( x ) = f -1 ( x ) , then which of the following could be the graph of
y = g ( x ) in the xy-plane?
(A)
(B)
(C)
(D)
131. The figures above show six data points plotted in the xy -plane, as well as the residual plot that results when the
regression M is used to model the given data. Which of the following statements about the regression model M is
best?
(A) The model M is exponential, and the model was appropriate.
(B) The model M is exponential, and the model was not appropriate.
(C) The model M is logarithmic, and the model was appropriate.
(D) The model M is logarithmic, and the model was not appropriate.
AP Style MCQ
Unit 2
Created by Bryan Passwater
132. After a concert date is announced, tickets begin to sell online. The number of tickets remaining is modeled by the
function S ( t ) = 301.8 - 65.72ln (1.3t + 7 ) , where S is the number of tickets remaining t hours after tickets begin
selling online. At what time t will there be 35 tickets remaining?
(A) 29.254
(B) 39.195
(C) 41.495
(D) 70.548
Topic 2.15: Semi-log Plots
133. The function f consists of 11 points in the xy -plane, as shown above. These 11 points are graphed using a semilog plot (not shown), in which the vertical axis is logarithmically scaled. Which of the following statements best
describe how these data will appear on the semi-log plot?
(A) The data will appear linear, because data that exhibit exponential behavior in the xy -plane display a linear when
graphed on a semi-log plot in which the vertical axis is logarithmically scaled.
(B) The data show no apparent pattern, because only logairthmic data will display a pattern when graphed on a semilog plot in which the vertical axis is logarithmically scaled.
(C) The data will appear exponential, because data whose outputs increase multiplicatively while the inputs increase
additively display an exponential pattern when graphed on a semi-log plot in which the vertical axis is
logarithmically scaled.
(D) The data will appear logarithmic, because data that exhibit exponential behavior in the xy -plane display a
logarithmic pattern when graphed on a semi-log plot in which the vertical axis is logarithmically scaled.
AP Style MCQ
Unit 2
Created by Bryan Passwater
134. The figure shows six points for the function f graphed on a semi-log plot, where the vertical axis is logarithmically
scaled. Which of the following could be f ( x ) ?
æ1ö
è2ø
(A) f ( x ) = 800 ç ÷
(B) f ( x ) = 800 ( 2 )
x
x
(C) f ( x ) = 800 - 2 x
(D) f ( x ) = log10 800 - ( log10 2 ) × x
æ1ö
è5ø
x
135. A data set that appears exponential is modeled by the function g given by g ( x ) = 6 × ç ÷ . The data are
represented using a semi-log plot, where the vertical axis is logarithmically scaled with the log base 10. Which of
the following gives the slope of the data as they appear in the semi-log plot?
(A) - ln 5
AP Style MCQ
(B) ln 5
(C) ln 6
(D)
Unit 2
1
5
Created by Bryan Passwater
𝑥
1
2
3
4
5
𝑓(𝑥)
12
35
108
325
980
136. The table gives values for a function f at selected values of x. Which of the following graphs could represent these
data in a semi-log plot, where the vertical axis is logarithmically scaled?
(A)
(B)
(C)
(D)
AP Style MCQ
Unit 2
Created by Bryan Passwater
𝑥
1
2
3
4
5
𝑔(𝑥)
813
366
165
74
33
137. The table gives values for a function 𝑔 at selected values of x. Which of the following graphs could represent these
data in a semi-log plot, where the vertical axis is logarithmically scaled?
(A)
(B)
(C)
(D)
AP Style MCQ
Unit 2
Created by Bryan Passwater
𝑥
ℎ(𝑥)
5
2
10
6
15
18
20
54
25
162
138. The table gives values for a function ℎ at selected values of x. Which of the following best describes how the data in
the table would appear if displayed using a semi-log plot, where the vertical axis is logarithmically scaled?
(A) The data would appear linear using a semi-log plot, because the function ℎ is best modeled using a logarithmic
function.
(B) The data would appear linear using a semi-log plot, because the function ℎ is best modeled using an exponential
function.
(C) The data would appear logarithmic using a semi-log plot, because the function ℎ is best modeled using an
exponential function.
(D) The data would appear logarithmic using a semi-log plot, because the function ℎ is best modeled using a
logarithmic function.
139. The figure shows five data points using a semi-log plot, where the vertical axis is logarithmically scaled. Which of
the following could describe the appearance of the data when graphed in the xy -plane?
(A) The data appear exponential and concave up.
(B) The data appear logarithmic and concave up.
(C) The data appear exponential and concave down.
(D) The data appear logarithmic and concave down.
AP Style MCQ
Unit 2
Created by Bryan Passwater
140. A data set is represented using a semi-log plot, where the vertical axis is logarithmically scaled appears linear. The
linear model for the semi-log plot is given by y = ( log10 2) x + log10 5. Which of the following functions could
represent the data set in the xy -plane?
(A) f ( x ) = 2 × 5x
(B) f ( x ) = 5 × 2x
(C) f ( x ) = 2 + 5x
(D) f ( x ) = 5 + 2 x
141. A data set is represented using a semi-log plot, where the vertical axis is logarithmically scaled with the natural
logarithm. On the semi-log plot, the data appear linear and can be modeled by y = ln 4 - x ( ln 3) . In the xy -plane,
the data can be modeled by the exponential function g ( x ) = ab x , where a and b are constants. What is the value
of b ?
(A) b = 4
(C) b =
(B) b = 3
4
3
(D) b =
1
3
142. The figures above show six data points in a semi-log plot, where the vertical axis is logarithmically scaled, as well as
the residual plot that results when the regression P is used to model the given data. Which of the following
statements about the regression model P is true?
(A) The model P is linear, and the model was appropriate.
(B) The model P is linear, and the model was not appropriate.
(C) The model P is exponential, and the model was appropriate.
(D) The model P is exponential, and the model was not appropriate.
AP Style MCQ
Unit 2
Created by Bryan Passwater