Answers2627 ALGEBRA II AFunction Inverses

Function Inverses — Unit test Answers

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For which pair of functions is ?

Question illustration
A
f(x) = 3 – 4x and g(x) = 16x – 3
B
f(x) = 6x2 and
Option B
C
and g(x) = 144x
Option C
D
f(x) = 4x and g(x) = 3x
2
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Which statement verifies that f(x) and g(x) are inverses of each other?

A
Option
Option A
B
and
Option B
C
Option
Option C
D
and
Option D
3

Mr. Valenzuela’s new bottle of shampoo contains 60 ounces of shampoo. He uses ounce of shampoo each time he washes his hair. Which equation can be used to find x, the number of washes after which 24 ounces will remain in the bottle?

Question illustration
A
One-fourth x minus 60 equals 24
Option A
B
60 minus one-fourth x equals 24
Option B
C
One-fourth x minus 24 equals 60
Option C
D
24 minus one-fourth x equals 60
Option D
4

If and , what is the degree of ?

Question illustration
A
2
B
3
C
5
D
6
5

If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of ?

Question illustration
A
all real values of x
B
all real values of x except x = 5
C
all real values of x except x = –5
D
all real values of x except x = 5 and x = –5
6

The graph of f(x) is shown below.If g(x) and f(x) are inverse functions, which graph represents g(x)?

Question illustration
A
On a coordinate plane, a curve opens up and to the left in quadrant 1. The curve starts at (0, 0) and curves up sharply through (2, 4).
Option A
B
On a coordinate plane, a curve opens down and to the left in quadrant 2. The curve starts at (0, 0) and gradually curves through (negative 4, 2).
Option B
C
On a coordinate plane, a curve opens open and to the left in quadrant 3. The curve starts at (0, 0) and curves gradually through (negative 4, negative 2).
Option C
D
On a coordinate plane, a curve opens up and to the left in quadrant 1. The curve starts at (0, 0) and curves up through (4, 1).
Option D
7

The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of ?

Question illustration
A
u(x) 0 and v(x) 2
Option A
B
x 0 and x cannot be any value for which u(x) 2
Option B
C
x 2 and x cannot be any value for which v(x) 0
Option C
D
u(x) 2 and v(x) 0
Option D
8

If the function has an inverse function, which statement must be true?

Question illustration
A
b not-equals 0
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?

A
The pool must have been empty for the entire interval.
B
The pool must have been the same depth at the start of the interval as it was at the end of the interval.
C
The pool must have been deeper at the end of the interval than it was at the start of the interval.
D
The pool must have been more shallow at the end of the interval than it was at the start of the interval.
10

The graph shows the distance in miles of a runner over x hours. What is the average rate of speed over the interval [9, 11]?

Question illustration
A
Two-fifths
Option A
B
1
C
2
D
Five-halves
Option D
11

Which function is the inverse of ?

Question illustration
A
f Superscript negative 1 Baseline (x) = negative one-fifth x + four-fifths
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

The equation |p| = 2 represents the total number of points that can be earned or lost during one turn of a game. Which best describes how many points can be earned or lost during one turn?

A
–2
B
2
C
0 or 2
D
–2 or 2
13

Rami is solving the equation for x .–6x – 1 = 5–6x – 1 1 = (5 1)–6x = 6–6x – 6 = 6 –6x = –1

Question illustration
A
should contain +; should contain ×
Option A
B
should contain +; should contain ÷
Option B
C
should contain –; should contain ×
Option C
D
should contain –; should contain ÷
Option D
14

The tables for f(x) and g(x) are shown below.xf(x)–5–11–21113529xg(x)–5–7–2–115513What is the value of (f – g)(5)?

A
–18
B
–4
C
16
D
42
15

Katie ordered candles that cost $3 each from a website. She was charged a flat shipping fee of $6 and no sales tax. If she spent a total of $54, which equation can be used to find c, the number of candles she ordered?

A
3c = 54
B
6c = 54
C
3c + 6 = 54
D
3c – 6 = 54
16

A cell phone carrier offers two plans for text messaging. Plan A costs $20 per month plus $0.05 per text. Plan B costs $10 per month plus $0.10 per text. For how many text messages per month are the plans the same cost?

A
20
B
30
C
200
D
300
17

Which system of equations is consistent and dependent?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
18

If k(x) = 5x – 6, which expression is equivalent to (k + k)(4)?

A
5(4 + 4) – 6
B
5(5(4) – 6) – 6
C
54 – 6 + 54 – 6
D
5(4) – 6 + 5(4) – 6
19

What is the point of intersection when the system of equations below is graphed on the coordinate plane?

Question illustration
A
(1, –3)
B
(–1, 3)
C
(1, 3)
D
(–1, –3)
20

Brandi is downloading music for her MP3 player. Albums cost $10 each, and singles cost $1 each. She wants to purchase at least 5 singles but wants to spend no more than $25 total. If Brandi purchases x albums and y singles, which of the following is a possible combination of albums and singles that Brandi could purchase and stay within her guidelines?

Question illustration
A
5 albums and 2 singles
B
2 albums and 5 singles
C
2 albums and 10 singles
D
10 albums and 2 singles

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