AnswersAL-PrecalculusCumulative Exam

Cumulative Exam — Cumulative exam Answers

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21
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The graph of f(x) = 4x3 – 13x2 + 9x + 2 is shown below. How many roots of f(x) are rational numbers?

Question illustration
A
0
B
1
C
2
D
3
22
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Which of the pairs of functions and their inverses will always have a domain and range of all real numbers?

A
a pair of linear functions with defined slopes
B
a cubic function and a cube root function
C
a quadratic function and a square root function
D
a logarithmic function and an exponential function
23

What is the solution to the equation ?

Question illustration
A
x = –3
B
x = –3 and x = 0
C
x = 0 and x = 3
D
x = 3
24

Which equation is represented by the graph below?

Question illustration
A
y = one-eighth e Superscript x
Option A
B
y = one-half e Superscript x
Option B
C
y = 2 e Superscript x
Option C
D
y = 8 e Superscript x
Option D
25

What is the exact value of ?

Question illustration
A
Negative StartFraction StartRoot 2 minus StartRoot 2 EndRoot EndRoot Over 4 EndFraction
Option A
B
Negative StartFraction StartRoot 2 + StartRoot 2 EndRoot EndRoot Over 4 EndFraction
Option B
C
Negative StartFraction StartRoot 2 minus StartRoot 2 EndRoot EndRoot Over 2 EndFraction
Option C
D
Negative StartFraction StartRoot 2 + StartRoot 2 EndRoot EndRoot Over 2 EndFraction
Option D
26

What is the true solution to

Question illustration
A
x = 5
Option A
B
x = 10
Option B
C
x = 50
Option C
D
x = 100
Option D
27

What are all the exact solutions of for ? Give your answer in radians.

Question illustration
A
mc017-3.jpg
Option A
B
and
Option B
C
and
Option C
D
, and
Option D
28

Suppose and sin(x) > 0. What is the value of tan(2x)?

Question illustration
A
Negative 5
Option A
B
Negative four-thirds
Option B
C
Four-thirds
Option C
D
2
29

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
30

The table below shows the number of days, y, needed to complete a project as a function of the number of full-time staff, x, working on the project. Which rational function best models the data in the table?People Working, xDays, y36218489612

A
mc019-1.jpg
Option A
B
mc019-2.jpg
Option B
C
mc019-3.jpg
Option C
D
mc019-4.jpg
Option D
31

Let csc(x) = , where . Which ratio has a value of ?

Question illustration
A
cos(x)
B
sin(x)
C
sec(x)
D
cot(x)
32

Which of the following is the graph of the function y = 4csc(x)?

A
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 12 to 4 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 3 at (pi by 2 comma negative 3) and (negative 3 pi by 2 comma negative 3) and y equals negative 5 at (3 pi by 2 comma negative 5) and (negative pi by 2 comma negative 5).
Option A
B
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 12 to 4 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals 5 at (pi by 2 comma 5) and (negative 3 pi by 2 comma 5) and y equals negative 3 at (3 pi by 2 comma 3) and (negative pi by 2 comma 3).
Option B
C
On a coordinate plane, the x axis ranges from negative pi to 3 pi with an interval of pi units and the y axis ranges from negative 8 to 8 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals 4 at (5 pi by 2 comma 4) and (pi by 2 comma 4) and y equals negative 4 at (3 pi by 2 comma negative 4) and (negative pi by 2 comma negative 4).
Option C
D
On a coordinate plane, the x axis ranges from negative pi to 3 pi with an interval of pi units and the y axis ranges from negative 8 to 8 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals 4 at (9 pi by 5 comma 4) and (pi by 5 comma 4) and y equals negative 4 at (14 pi by 5 comma negative 4) and (negative 4 pi by 5 comma negative 4).
Option D
33

Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction (y + 1) (y minus 1) Over y squared EndFraction
Option A
B
StartFraction y + 1 Over y minus 1 EndFraction
Option B
C
StartFraction y minus 1 Over y + 1 EndFraction
Option C
D
StartFraction y squared Over (y + 1) (y minus 1) EndFraction
Option D
34

The table shows several points for function j(t).

Question illustration
A
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 8, 10, 17. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries negative 1, negative 2, negative 10, negative 250.
Option A
B
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 8, 10, 17. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 0.5, 0.1, 0.004.
Option B
C
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 2, 10, 250. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 0.5, 0.1, 0.004.
Option C
D
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 2, 10, 250. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 8, 10, 17.
Option D
35

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
36

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 down and to the left in quadrants 3 and 4.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 3, 4, and 1.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 4 and 1.
Option D
37

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

Question illustration
A
x – 4
B
x – 2
C
x + 2
D
x + 4
38

Which statements accurately compare the functions in the graph? Select two options.

A
Neither function has a maximum value.
B
The functions share a y-intercept of –1.
C
The functions share an x-intercept of 1.
D
Both functions have a range of all real numbers.
E
Both functions have a domain of all real numbers.
39

Which is equivalent to cos-1(0)? Give your answer in radians.

A
0
B
mc005-1.jpg
Option B
C
mc005-2.jpg
Option C
D
mc005-3.jpg
Option D
40

Consider the function f(x) = . What transformation results in g(x)?

Question illustration
A
Translate units left and 7 units up.
Option A
B
Translate units right and 7 units up.
Option B
C
Translate units left and 7 units down.
Option C
D
Translate units right and 7 units down.
Option D

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