AnswersAP Calculus AB - MA5186 ATechnology Corner

Technology Corner — Unit test Answers

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Let f be a function defined as f(x) = 2x + log2x over the interval [1, 2]. What conclusion can be made about the value of k such that f(k) = 4?

A
The value of k must be 18.
B
The value of k must be between 1 and 2.
C
No conclusion can be made about k because 1 < 2 < 4.
D
No conclusion can be made about k because f(x) is not continuous over the interval.
2
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The graph of f(x) = is continuous for

Question illustration
A
all real numbers.
B
all real numbers where x ≠ 0.
C
all real numbers where –1 ≤ x ≤ 1.
D
all real numbers where x ≤ –1 or x ≥ 1.
3

Use the four functions to answer the question.I. f(x) = II. f(x) = III. f(x) = IV. f(x) = For which function does not exist?

Question illustration
A
I
B
II
C
III
D
IV
4

A particle travels along the x-axis such that its position at time t is given by the function x(t) = 2t2 + t. What is the average speed of this particle over the interval 2 ≤ t ≤ 10?

A
4
B
25
C
32
D
200
5

Let f(x) = and g(x) = . For which value of x does f(g(x)) have a discontinuity?

Question illustration
A
1
B
2
C
3
D
4
6

Which table identifies all vertical and horizontal asymptotes, if any, of f(x) = ?

Question illustration
A
A 2-column table with 2 rows. Column 1 has entries vertical asymptote (s), horizontal asymptote (s). Column 2 has entries x = 2, none.
Option A
B
A 2-column table with 2 rows. Column 1 has entries vertical asymptote (s), horizontal asymptote (s). Column 2 has entries x = negative 2 and x = 2, none.
Option B
C
A 2-column table with 2 rows. Column 1 has entries vertical asymptote (s), horizontal asymptote (s). Column 2 has entries x = 2, y = 0.
Option C
D
A 2-column table with 2 rows. Column 1 has entries vertical asymptote (s), horizontal asymptote (s). Column 2 has entries x = negative 2 and x = 2, y = 0.
Option D
7

Use this graph of a function.For how many values of x is the function discontinuous on the interval [–4, 4]?

Question illustration
A
1
B
2
C
3
D
4
8

Let f be a function such that ≤ f(x) ≤ for all –2 ≤ x ≤ 2. What is ?

Question illustration
A
The limit is 0.
B
The limit is 1.
C
The limit does not exist.
D
The limit cannot be found because f(x) is unknown.
9

Which function is an extended function for f(x) = that is continuous for all values of x?

Question illustration
A
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row negative 2, x = negative 1, 1.
Option A
B
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row negative 2, x = 1.
Option B
C
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row 4, x = negative 1, 1.
Option C
D
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row 4, x = 1.
Option D
10

An end behavior model for f(x) = is g(x) =

Question illustration
A
2x2.
B
2x3.
C
2x4.
D
2x6.
11

A graphing calculator can be used on this question.Which type of discontinuity exists at x = 0 for the function f(x) = cos ?

Question illustration
A
jump
B
infinite
C
oscillating
D
removable
12

The equation of the normal line of the function f(x) = at x = –1 is

Question illustration
A
y = –2x – 1.
B
y = –2x + 1.
C
y = .
Option C
D
y = .
Option D
13

What is the equation of the line tangent to the function f(x) = 1 – x2 at x = –3?

A
y = 6x + 10
B
y = 6x + 26
C
y = –6x – 8
D
y = –6x – 26
14

What is ?

Question illustration
A
0
B
1
C
e
D
nonexistent
15

Let f and g be functions such that . If k ≠ 0, then

Question illustration
A
0.
B
1.
C
k.
D
k2.
16

What is ?

Question illustration
A
0
B
One-half
Option B
C
2
D
nonexistent
17

What is the average rate of change of f(x) = esin x over the interval ?

Question illustration
A
StartFraction e minus 1 Over pi EndFraction
Option A
B
StartFraction 1 minus e Over pi EndFraction
Option B
C
StartFraction 2 (e minus 1) Over pi EndFraction
Option C
D
StartFraction 2 (1 minus e) Over pi EndFraction
Option D
18

The slope of the tangent line to the function f(x) = at x = –5 is

Question illustration
A
–1.
B
.
Option B
C
.
Option C
D
8.
19

An object travels along the x-axis such that its position at time t is given by the function . How many times greater is the instantaneous speed of the object at t = 7 than the average speed of the object over the interval 1 ≤ t ≤ 7?

Question illustration
A
StartFraction 1 Over 24 EndFraction
Option A
B
One-fourth
Option B
C
4
D
24
20

Use this graph of function f.Which table identifies the one-sided and two-sided limits of function f at x = 2?

Question illustration
A
A 2-column table with 3 rows. Column 1 has entries Limit of f (x) as x approaches 2 minus, Limit of f (x) as x approaches 2 plus, limit of f (x) as x approaches 2. Column 2 has entries 1, 4, 1.
Option A
B
A 2-column table with 3 rows. Column 1 has entries Limit of f (x) as x approaches 2 minus, Limit of f (x) as x approaches 2 plus, limit of f (x) as x approaches 2. Column 2 has entries 4, 1, 1.
Option B
C
A 2-column table with 3 rows. Column 1 has entries Limit of f (x) as x approaches 2 minus, Limit of f (x) as x approaches 2 plus, limit of f (x) as x approaches 2. Column 2 has entries 4, 1, nonexistent.
Option C
D
A 2-column table with 3 rows. Column 1 has entries Limit of f (x) as x approaches 2 minus, Limit of f (x) as x approaches 2 plus, limit of f (x) as x approaches 2. Column 2 has entries nonexistent, nonexistent, nonexistent.
Option D

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