AnswersTX-Precalculus ACumulative Exam

Cumulative Exam — Cumulative exam Answers

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41
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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
42
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For the expression , which sum represents the correct form of the partial fraction decomposition?

Question illustration
A
StartFraction A x + B Over 3 x squared minus 4 EndFraction + StartFraction C x + D Over (3 x squared minus 4) squared EndFraction
Option A
B
StartFraction A Over 3 x squared minus 4 EndFraction + StartFraction B Over (3 x squared minus 4) squared EndFraction
Option B
C
StartFraction A x + B Over (3 x squared minus 4) squared EndFraction + StartFraction C x + D Over (3 x squared minus 4) squared EndFraction
Option C
D
StartFraction A Over (3 x squared minus 4) squared EndFraction + StartFraction B Over (3 x squared minus 4) squared EndFraction
Option D
43

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
45

Given: < A < and , < B < What is the value of cos(A – B)?

Question illustration
A
Negative StartFraction 2 StartRoot 5 EndRoot Over 25 EndFraction
Option A
B
Negative StartFraction StartRoot 5 EndRoot Over 5 EndFraction
Option B
C
StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction
Option C
D
StartFraction 11 StartRoot 5 EndRoot Over 25 EndFraction
Option D
46

What is the solution set to log(x + 7) > log3x?

A
(–∞, 3)
B
(–7, 0)
C
(0, 3)
D
(3, ∞)
47

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)
48

The polynomial equation has complex roots . What is the other root? Use a graphing calculator and a system of equations.

Question illustration
A
–9
B
–1
C
0
D
1
49

Information about two gears is shown in the table.Which statements compare the angular and linear velocities of the gears? Check all that apply.Gear 1 has a greater angular velocity than Gear 2.Gear 1 has a lesser angular velocity than Gear 2.Gear 1 has a greater linear velocity than Gear 2.Gear 1 has a lesser linear velocity than Gear 2.

Question illustration
A
Gear 1 has a greater angular velocity than Gear 2.
B
Gear 1 has a lesser angular velocity than Gear 2.
C
Gear 1 has a greater linear velocity than Gear 2.
D
Gear 1 has a lesser linear velocity than Gear 2.
50

What is the solution of ?

Question illustration
A
–8
B
–6
C
8
D
9
51

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.
52

What is the quotient and remainder, written as partial fractions, of ?

Question illustration
A
Option
Option A
B
4 x minus 1 + StartFraction 2 Over x + 1 EndFraction minus StartFraction 7 Over x + 2 EndFraction
Option B
C
4 x minus 1 + StartFraction 2 Over x + 1 EndFraction + StartFraction 3 Over x + 2 EndFraction
Option C
D
4 x minus 1 + StartFraction 2 Over x + 1 EndFraction minus StartFraction 3 Over x + 2 EndFraction
Option D
53

Consider the graph of f(x) = 5x 6 – 5x 5 – x 4.

Question illustration
A
One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than x less-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
Option A
B
One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than-or-equal-to x less-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
Option B
C
x less-than one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
Option C
D
x less-than-or-equal-to one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
Option D
54

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
55

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).
56

Which expression is equivalent to ?

Question illustration
A
StartFraction negative 1 minus tangent (2 x) Over 1 minus (negative 1) (tangent (2 x) ) EndFraction
Option A
B
StartFraction negative 1 minus tangent (2 x) Over 1 + (negative 1) (tangent (2 x) ) EndFraction
Option B
C
StartFraction 1 minus tangent (2 x) Over 1 + (1) (tangent (2 x) ) EndFraction
Option C
D
StartFraction 1 + tangent (2 x) Over 1 minus (1) (tangent (2 x) ) EndFraction
Option D
57

What function is graphed below?

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
58

Sandra graphed the system of equations that can be used to solve . What are the roots of the polynomial equation?

Question illustration
A
–12, 12
B
–4, 3
C
–3, 4
D
–1, 1
59

Which of the following describes the zeroes of the graph of f(x) = –x5 + 9x4 – 18x3?

A
0 with multiplicity 3, –3 with multiplicity 2, and –2 with multiplicity 1
B
0 with multiplicity 3, 3 with multiplicity 1, and 6 with multiplicity 1
C
0 with multiplicity 3, 3 with multiplicity 2, and 2 with multiplicity 1
D
0 with multiplicity 3, –3 with multiplicity 1, and –6 with multiplicity 1
60

What is the value of x in ?

Question illustration
A
Negative StartFraction 2 pi Over 3 EndFraction
Option A
B
Negative StartFraction pi Over 6 EndFraction
Option B
C
StartFraction 2 pi Over 3 EndFraction
Option C
D
StartFraction 7 pi Over 6 EndFraction
Option D

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