AnswersTX-Precalculus AUnit Test

Unit Test — Unit test Answers

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1
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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
2
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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.
3

A function and its inverse are shown on the same graph.

Question illustration
A
The slope of f–1(x) is the same as the slope of f(x).
B
The slope of f–1(x) is the opposite as the slope of f(x).
C
The x-intercept of f–1(x) is the same as the y-intercept of f(x).
D
The x-intercept of f–1(x) is half of the y-intercept of f(x).
4

The function is the result of the composition f(g(x)). If g(x) = x2 + 1, what is f(x)?

Question illustration
A
f (x) = StartFraction 1 Over StartRoot x EndRoot
Option A
B
Option
Option B
C
f (x) = StartFraction 1 Over x + 1 EndFraction
Option C
D
f (x) = StartFraction 1 Over x squared + 1 EndFraction
Option D
5

Consider the function m(t) = .Angie states that the additive inverse is p(t) = and the multiplicative inverse is r(t) = . Is one (or both) of Angie’s conclusions correct?

Question illustration
A
Angie is correct about both inverses.
B
Angie is correct about neither inverse.
C
Angie is correct about the additive inverse only.
D
Angie is correct about the multiplicative inverse only.
6

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)
7

Which tables could be used to verify that the functions they represent are inverses of each other? Select two options.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
E
Option
Option E
8

Which two transformations must be applied to the graph of y = ln(x) to result in the graph of y = –ln(x) + 64?

A
reflection over the x-axis, plus a vertical translation
B
reflection over the y-axis, plus a vertical translation
C
reflection over the x-axis, plus a horizontal translation
D
reflection over the y-axis, plus a horizontal translation
9

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.
10

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.
11

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
12

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
13

Review the graph of function h(x).

Question illustration
A
(2, 4)
B
(0, one-half)
Option B
C
(0, 1)
D
(–5, 1)
14

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)
15

Consider . What value(s) of x would make f(g(x)) and g(f(x)) commutative?

Question illustration
A
x greater-than-or-equal-to 1 or x less-than-or-equal-to negative 1
Option A
B
Negative 1 less-than-or-equal-to x less-than-or-equal-to 1
Option B
C
any value of x
D
no value of x
16

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
17

Consider the function h(x) =x2 – 12x + 58.Which represents a domain restriction and the corresponding inverse function?

A
x ≥ 6; h–1(x) =
Option A
B
x ≥ 6; h–1(x) =
Option B
C
x ≥ 12; h–1(x) =
Option C
D
x ≥ 12; h–1(x) =
Option D
18

The function h(x) = 12x8 + 49 is an even function. Which transformation of h(x) would result in a function that is neither even nor odd?

A
reflection over the x-axis
B
vertical stretch by a factor of 7
C
translation 8 units to the right
D
horizontal compression by a factor of
19

A linear function and its inverse are given. Which tables could be used to verify that the functions are inverses of each other? Select two options.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
E
Option
Option E
20

Which is the graph of ?

Question illustration
A
On a coordinate plane, a curve starts at (0, 2) and curves up through (30, 5) and (70, 6).
Option A
B
On a coordinate plane, a curve starts at (0, 0) and curves up through (50, 3) and (80, 3.5).
Option B
C
On a coordinate plane, a curve starts at (0, 0) and curves up through (60, 5) and (80, 5.5).
Option C
D
On a coordinate plane, a curve starts at (0, 0) and curves up through (60, 8) and (70, 8.4).
Option D

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