Answers25-26 KCS21 Precalculus ICCumulative Exam

Cumulative Exam — Cumulative exam Answers

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Functions f(x) and g(x) are composed to form . If , what is the value of a?

Question illustration
A
0
B
–1
C
–2
D
–4
2
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What is written as a single logarithm?

Question illustration
A
log Subscript 2 Baseline left-bracket StartFraction x cubed Over (StartFraction 3 Over x + 4 EndFraction) EndFraction Right-bracket
Option A
B
log Subscript 2 Baseline (StartFraction 3 x cubed Over x + 4 EndFraction)
Option B
C
log Subscript 2 Baseline left-bracket (StartStartFraction x cubed Over 3 EndFraction) Over x + 4 EndEndFraction Right-bracket
Option C
D
log Subscript 2 Baseline (StartFraction x cubed Over 3 + (x + 4) EndFraction)
Option D
3

What is the vertical shift of the graph of the parent cosecant function to the graph of the function below?

Question illustration
A
1 unit down
B
2 units down
C
3 units down
D
4 units down
4

Consider the function f(x) = |x|. Let g(x) = |–4(x – 7)|.Which shows the graphs of f(x) and g(x)?

A
On a coordinate plane, y = g (x) opens up and goes through (negative 3, 4), has a vertex at (negative 2, 0) and goes through (0, 7). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
Option A
B
On a coordinate plane, y = g (x) opens up and goes through (6, 4), has a vertex at (7, 0) and goes through (8, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
Option B
C
On a coordinate plane, y = g (x) opens down and goes through (6, negative 4), has a vertex at (7, 0) and goes through (8, negative 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
Option C
D
On a coordinate plane, y = g (x) opens up and goes through (negative 8, 4), has a vertex at (negative 7, 0) and goes through (negative 6, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).
Option D
5

What is the binomial expansion of (x + 2y)7?

A
2x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + 2y7
B
x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + y7
C
x7 + 7x6y + 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7
D
x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7
6

Which transformations to the graph of y = ex would result in the graph of y = ex + 34 – 27?

A
translation of 34 units right and 27 units up
B
translation of 34 units right and 27 units down
C
translation of 34 units left and 27 units up
D
translation of 34 units left and 27 units down
7

Which of the following is the inverse of ?

Question illustration
A
y = log Subscript one-twelfth Baseline x
Option A
B
y = log Subscript 12 Baseline StartFraction 1 Over x EndFraction
Option B
C
y = log Subscript x Baseline 12
Option C
D
y = log Subscript 12 Baseline x
Option D
8

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?f(x) = (x3 – 3x + 1)2

A
2 roots
B
3 roots
C
6 roots
D
9 roots
9

Review the table showing the percentage of contaminants remaining in a water sample after passing through each round of filters.Round% of Contaminants Left in Water Sample01001152230.3

A
6.3% of the contaminants remain in the water sample after each round of filters.
B
14.9% of the contaminants remain in the water sample after each round of filters.
C
6.3% of the remaining contaminants are removed from the water sample after each round of filters.
D
14.9% of the remaining contaminants are removed from the water sample after each round of filters.
10

If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?

A
On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 5) and crosses the x-axis at (1, 0).
Option A
B
On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 4), has a vertex at (0, 5), and goes through (2, negative 2)
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 3, 7), has a vertex at (negative 1, 2), and goes through (0, 5).
Option C
D
On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
Option D
11

Which is an x-intercept of the graph of the function ?

Question illustration
A
(StartFraction pi over 6 EndFraction, 0)
Option A
B
(StartFraction pi over 3 EndFraction , 0)
Option B
C
(3pi, 0)
Option C
D
(6pi, 0)
Option D
12

To produce the graph of the function , what transformations should be applied to the graph of the parent function ?

Question illustration
A
a horizontal compression to produce a period of and a vertical compression
Option A
B
a horizontal compression to produce a period of and a vertical stretch
Option B
C
a horizontal stretch to produce a period of and a vertical compression
Option C
D
a horizontal stretch to produce a period of and a vertical stretch
Option D
13

Which expression is equivalent to ?

Question illustration
A
x Superscript one-half Baseline y Superscript 4
Option A
B
x Superscript one-eighth Baseline y Superscript 8
Option B
C
x Superscript one-fourth Baseline y Superscript 8
Option C
D
x Superscript one-fourth Baseline y Superscript 4
Option D
14

What is the value of ?

Question illustration
A
3
B
5
C
15
D
25
15

The graph of a logarithmic function is shown below.What is the domain of the function?

Question illustration
A
x < 0
B
x > 0
C
x < 1
D
all real numbers
16

The acceleration y, in meters per second squared, of an object after x seconds is given by y = .During the first 10 seconds, over which intervals is the acceleration increasing?

Question illustration
A
(2, 6)
B
(4, 8)
C
(0, 2) and (6, 10)
D
(0, 4) and (8, 10)
17

Which expression is equivalent to ?

Question illustration
A
RootIndex 4 StartRoot 2 cubed EndRoot
Option A
B
StartRoot 2 Superscript 5 EndRoot
Option B
C
RootIndex 4 StartRoot 4 cubed EndRoot
Option C
D
StartRoot 4 Superscript 5 EndRoot
Option D
18

The height of a tennis ball tossed into the air is modeled by h(x) = 40x – 16x 2, where x is elapsed time in seconds.During what time interval will the tennis ball be at least 15 feet above the ground?

A
x > 0.5 seconds and x > 2.04 seconds
B
x > 0.5 seconds and x ≤ 2.04 seconds
C
x ≥ 0.5 seconds and x > 2.04 seconds
D
x ≥ 0.5 seconds and x ≤ 2.04 seconds
19

At which x-value does the cosine function attain a maximum value?

A
x = 0
B
x = StartFraction pi Over 2 EndFraction
Option B
C
x = 1
D
x = StartFraction 3 pi Over 2 EndFraction
Option D
20

The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?

Question illustration
A
1.5 days
B
2.5 days
C
9.4 days
D
21.1 days

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