AnswersAL-PrecalculusCumulative Exam

Cumulative Exam — Cumulative exam Answers

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If the function y = sin(x) is transformed to y = sin(2x), how does the graph change?

A
It is stretched vertically.
B
It is compressed vertically.
C
It is stretched horizontally.
D
It is compressed horizontally.
2
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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
3

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
4

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)
5

By what approximate factor is the intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3?M = the magnitude of an earthquakeI = the intensity of an earthquakeI0 = the smallest seismic activity that can be measured, which is 1

Question illustration
A
1.01
B
1.21
C
1.26
D
10.44
6

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.
Option D
7

The function that represents the average cost per person, including transportation, to a museum is . Which statement is true about the graph of the function?

Question illustration
A
The horizontal asymptote y = 0 means the cost approaches zero as the number of people increases.
B
The horizontal asymptote y = 8 means the average cost approaches $8 as the number of people increases.
C
The vertical asymptote x = 0 means the cost approaches zero as the number of people increases.
D
The vertical asymptote x = 8 means the cost approaches zero as the number of people increases.
8

Given the function g(x) = 41x3 + a for some constant a, which describes the inverse function g–1(x)?

A
no restriction on the domain of g(x); inverse is g–1(x) =
Option A
B
no restriction on the domain of g(x); inverse is g–1(x) =
Option B
C
domain of g(x) restricted to x ≥ 0; inverse is g–1(x) =
Option C
D
domain of g(x) restricted to x ≥ 0; inverse is g–1(x) =
Option D
9

What is the factored form of the binomial expansion 625x4 – 3,000x3y + 5,400x2y2 – 4,320xy3 + 1,296y4?

A
(5x – 6y)4
B
(5x + 6y)4
C
(25x – 36y)2
D
(25x + 36y)2
10

What are the potential solutions of

Question illustration
A
mc019-2.jpg
Option A
B
mc019-3.jpg
Option B
C
mc019-4.jpg
Option C
D
mc019-5.jpg
Option D
11

According to the Rational Root Theorem, is a potential rational root of which function?

Question illustration
A
f(x) = 4x4 – 7x2 + x + 25
B
f(x) = 9x4 – 7x2 + x + 10
C
f(x) = 10x4 – 7x2 + x + 9
D
f(x) = 25x4 – 7x2 + x + 4
12

Amanda has a job that pays $35 per hour for the first 40 hours worked each week, plus 1.5 times this hourly rate for work done over 40 hours. Suppose Amanda works 50 hours this week. How much will she earn before taxes?

A
$1,575
B
$1,750
C
$1,925
D
$2,625
13

What is the quotient?

Question illustration
A
(t + 3) squared
Option A
B
(t + 4) squared
Option B
C
StartFraction 1 Over (t + 4) squared EndFraction
Option C
D
StartFraction 1 Over (t + 3) squared EndFraction
Option D
14

What is the difference?

Question illustration
A
StartFraction x squared + 4 x minus 1 Over x (x + 2) EndFraction
Option A
B
StartFraction x squared + 4 x + 1 Over x (x + 2) EndFraction
Option B
C
StartFraction 4 Over negative 1 (x squared + x minus 2) EndFraction
Option C
D
StartFraction x squared + 6 x + 1 Over x (x + 2) EndFraction
Option D
15

The tables show linear functions representing the cost for purchasing different amounts of broccoli and cauliflower.

Question illustration
A
The broccoli function has the greater slope, which shows that the cost per pound of broccoli is less than the cost per pound of cauliflower.
B
The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.
C
The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is less than the cost per pound of broccoli.
D
The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is greater than the cost per pound of broccoli.
16

What is the solution to

Question illustration
A
mc014-2.jpg
Option A
B
mc014-3.jpg
Option B
C
mc014-4.jpg
Option C
D
mc014-5.jpg
Option D
17

Review the graph.

Question illustration
A
The period of the graph is
Option A
B
The amplitude of the graph is 2 units.
C
The domain of the graph is the set of x-values from –3 to 3, inclusive.
D
The graph represents a reflection over the x-axis of the function y = 3sin(2x).
18

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
19

Which expression is equivalent to ?

Question illustration
A
StartFraction 2 (a + 1) squared Over a cubed EndFraction
Option A
B
6a
C
2a
D
StartFraction 6 a squared Over a + 1 EndFraction
Option D
20

The graph below shows the function .Which statement is true?

Question illustration
A
There is a hole at x = 3 and an asymptote at x = –1.
B
There is an asymptote at x = –1 and no hole.
C
There is a hole at x = 3 and no asymptote.
D
There is an asymptote at x = 3 and a hole at x = –1.

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