AnswersAL-Algebra II with StatisticsUnit Test

Unit Test — Unit test Answers

25 verified answers
1
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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
2
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Which tables could be used to verify that the functions they represent are inverses of each other? Select two options.

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
E
Option
Option E
3

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
4

A factory produces 1,250,000 toys each year. The number of toys is expected to increase by about 150% per year. Which model can be used to find the number of toys, n (in millions), being produced in t years?

A
,
Option A
B
n = 1.5 t squared + 1.25
Option B
C
n = 1.5 t + 1.25
Option C
D
n = 1.25 times 2.5 Superscript t
Option D
5

Consider the functions f(x) = 3x2, , and h(x) = 3x.Which statements accurately compare the domain and range of the functions? Select two options.All of the functions have a unique range.The range of all three functions is all real numbers.The domain of all three functions is all real numbers.The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.The domain of f(x) and h(x) is all real numbers, but the domain of g(x) is all real numbers except 0.

Question illustration
A
All of the functions have a unique range.
B
The range of all three functions is all real numbers.
C
The domain of all three functions is all real numbers.
D
The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.
E
The domain of f(x) and h(x) is all real numbers, but the domain of g(x) is all real numbers except 0.
6

The tables show functions representing the path of two rockets launched by different science lab groups.

Question illustration
A
Since the maximums occurred at the same x-value, the rockets followed the same path.
B
Since the x-intercepts are the same for both functions, the rockets followed the same path.
C
The rockets were in the air for the same amount of time, but the rocket for group B went higher in the air.
D
The rockets traveled the same height in the air, but the rocket for group B was in the air for a longer time.
7

If , what is f(5.9)?

Question illustration
A
9
B
10
C
11
D
12
8

The graph below represents c, the amount a phone company charges, based on m, the number of minutes the customer uses each month. If there are a maximum of 44,640 minutes in a month, which equation best represents the phone company’s monthly charges?

Question illustration
A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
9

A city manager made the graph below to represent the number of passengers that city buses can carry, where the number of passengers is represented by x, and the number of buses by y.If all city buses carry the same number of passengers, what is the least number of buses needed to carry 710 passengers?

Question illustration
A
5
B
10
C
11
D
12
10

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.
11

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.
12

Which piecewise relation defines a function?

A
mc008-1.jpg
Option A
B
mc008-2.jpg
Option B
C
mc008-3.jpg
Option C
D
mc008-4.jpg
Option D
13

Which characteristics do the functions have in common? Select two options.

A
range
B
domain
C
minimum
D
x-intercept
E
y-intercept
14

Which statements can be used to compare the characteristics of the functions? Select three options.

A
f(x) has the greatest maximum.
B
h(x) has the greatest x-intercept.
C
g(x) has the smallest minimum value.
D
All three functions share the same domain.
E
All three functions share the same y-intercept.
15

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}
16

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).
17

The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height in feet. What is the maximum height the rocket reaches?

Question illustration
A
16 ft
B
36 ft
C
48 ft
D
144 ft
18

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
19

Which of the following accurately shows the range of the function defined below?

Question illustration
A
mc025-2.jpg
Option A
B
mc025-3.jpg
Option B
C
[3, 6]
D
mc025-4.jpg
Option D
20

A store uses the expression –2p + 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere from $9 to $15. Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue = price number of backpacks.)

Question illustration
A
$9.00 per backpack gives the maximum revenue; the maximum revenue is $32.00.
B
$12.00 per backpack gives the maximum revenue; the maximum revenue is $312.00.
C
$12.50 per backpack gives the maximum revenue; the maximum revenue is $312.50.
D
$15.00 per backpack gives the maximum revenue; the maximum revenue is $20.00.

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