Answers2025-2026 FBISD - Precalculus A CRMonomial Functions

Monomial Functions — Unit test Answers

23 verified answers
1
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The graph models the heights, in feet, of two objects dropped from different heights after x seconds.

Question illustration
A
g(x) = f(x) – 5
B
g(x) = f(x – 5)
C
g(x) = f(x) + 5
D
g(x) = f(x + 5)
2
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Which best describes the end behavior of ?

Question illustration
A
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
B
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
C
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
D
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
3

Consider the tables created using an initial investment of $1,000 and quarterly compounding of interest.Table A represents the function that models the total amount of one investment, a(x), based on the annual interest rate, x, as a percent.Table B represents the function that models the interest rate, r(d), as a percent, based on the total amount at the end of the investment, d.

Question illustration
A
The functions are inverses because the domain of Table A is the same as the range of Table B.
B
The functions are inverses because the range of Table A is different from the domain of Table B.
C
The functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (x, y) for the other function.
D
The functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function.
4

In a certain country, a letter up to 1 ounce requires postage in the amount of $0.42, and each additional ounce (or fraction of an ounce) has an additional cost. The function below represents the cost of mailing one letter with a weight of x ounces in this country.Josiah has two letters. The first weighs 2.9 ounces, and the second weighs 4.1 ounces. What is the total amount Josiah can expect to pay for postage?

Question illustration
A
$1.62
B
$1.64
C
$1.84
D
$2.04
5

Which statement identifies how to show that j(x) = 11.6ex and k(x) = In are inverse functions?

Question illustration
A
All that needs to be shown is that j(k(x)) equals x.
B
All that needs to be shown is that j(k(x)) equals 1.
C
It must be shown that both j(k(x)) and k(j(x)) equal x.
D
It must be shown that both j(k(x)) and k(j(x)) equal 1.
6

What are the domain and range of the step function below?

Question illustration
A
domain = {all real numbers}, range = {all real numbers}
B
domain = {all real numbers}, range = {...–4, –1, 2, 5, ...}
C
domain = {...–5, –2, 1, 4, ...}, range = {...–4, –1, 2, 5, ...}
D
domain = {all integers}, range = {all real numbers}
7

Consider the function. Which conclusions can be drawn about f–1(x)? Select two options.f–1(x) has a slope of .f–1(x) has a restricted domain.f–1(x) has a y-intercept of (0, –36).f–1(x) has an x-intercept of (–36, 0).f–1(x) has a range of all real numbers.

Question illustration
A
f–1(x) has a slope of .
Option A
B
f–1(x) has a restricted domain.
C
f–1(x) has a y-intercept of (0, –36).
D
f–1(x) has an x-intercept of (–36, 0).
E
f–1(x) has a range of all real numbers.
8

Under which conditions does the commutative property apply to compositions of f(x) and g(x)?

A
when f(g(x)) and g(f(x) are inverse functions
B
when f(g(x)) and g(f(x) are equal for at least one value of x
C
when f(g(x)) and g(f(x) are equal for all values of x
D
when f(g(x)) and g(f(x) are not inverse functions
9

A telemarketer earns a base salary of $3,000 per month, plus an annual bonus of 2.5% of total sales above $250,000. Which function represents the annual salary for total sales of x dollars, where x is greater than $250,000?

A
S(x) = 3,000 + 0.025(x – 250,000)
B
S(x) = 3,000 + 2.5(x – 250,000)
C
S(x) = 12(3,000) + 0.025(x – 250,000)
D
S(x) = 12(3,000) + 2.5(x – 250,000)
10

Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?

Question illustration
A
f(x) = x2(x – a)2(x – b)4(x – c)
B
f(x) = x3(x – a)3(x – b)(x – c)2
C
f(x) = x4(x – a)(x – b)3(x – c)3
D
f(x) = (x – a)2(x – b)(x – c)6
11

Which expression is a possible leading term for the polynomial function graphed below?

Question illustration
A
–4x8
B
–4x5
C
4x5
D
4x8
12

Which graph represents a function that has the domain (–∞, –4) ⋃ (–4, 3) ⋃ (3, ∞), has a y-intercept at (0, 3), and is increasing on the interval (0, 4)?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
13

Which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)?

A
vertical translation
B
horizontal translation
C
reflection over the x-axis
D
reflection over the y-axis
14

What is the domain of the function graphed below?

Question illustration
A
mc023-2.jpg
Option A
B
mc023-3.jpg
Option B
C
mc023-4.jpg
Option C
D
mc023-5.jpg
Option D
15

If , what is f(5.9)?

Question illustration
A
9
B
10
C
11
D
12
16

Identify the graph of the rational function with an x-intercept at (–4, 0) and (4, 0), a vertical asymptote at x = 2, and an oblique asymptote at y = x + 2.

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
17

The equation of the piecewise defined function f(x) is below. What is the value of f(1)?

Question illustration
A
f(1) = –2
B
f(1) = –1
C
f(1) = 2
D
f(1) = 3
18

Which statement describes the function y = axn when a = 1 and n is odd?

A
The graph opens down.
B
The graph is symmetric about the origin.
C
The graph does not pass through the origin.
D
The graph has more than one x intercept.
19

Consider the function h(x) = . Which graph shows h(2x) + 4?

Question illustration
A
On a coordinate plane, a curve opens up and to the right in quadrants 1 and 4. It goes through (0.5, 1), (1, negative 2), and (2, negative 3). Another curve opens down and to the left in quadrant 3. It goes through (negative 4, negative 4.5) and (negative 2, negative 5).
Option A
B
On a coordinate plane, a curve opens up and to the right in quadrants 1 and 4. It approaches the y-axis in quadrant 1, and then curves down through (0.5, negative 3) and then approaches y = negative 4. Another curves opens down and to the left in quadrant 3. It approaches y = negative 4 and then curves down through (negative 1, negative 4.5).
Option B
C
On a coordinate plane, a curve opens up and to the right in quadrant 1. It goes through (2, 5) and (3, 4.5). Another curve opens down and to the left in quadrants 2 and 3. It goes through (negative 1, 2) and curves down through (negative 0.5, negative 1).
Option C
D
On a coordinate plane, a curve opens up and to the right in quadrant 1. It goes through (1, 4.5) and (4, 4). Another curve opens down and to the left in quadrants 2 and 3. It approaches y = 4 and then curves down and approaches the y-axis in quadrant 3.
Option D
20

Which statement describes the inverse of m(x) = x2 – 17x?

A
The domain restriction x ≥ results in m–1(x) = .
Option A
B
The domain restriction x ≥ results in m–1(x) = .
Option B
C
The domain restriction x ≥ results in m–1(x) = .
Option C
D
The domain restriction x ≥ results in m–1(x) = .
Option D

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