AnswersVA-Mathematical AnalysisStep Functions

Step Functions — Unit test Answers

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1
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Edmundo used a number line to show the solution for the inequality . Which number line shows the solution?

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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A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach infinity. To which family of functions might the described function belong?

A
reciprocal
B
square root
C
exponential
D
quadratic
3

Elise, Jake, Malik, and Xiao each solved the same inequality.Elise’s WorkJake’s WorkMalik’s WorkXiao’s Workno solutionall real numbersWhose work is correct?

Question illustration
A
Elise’s work
B
Jake’s work
C
Malik’s work
D
Xiao’s work
4

What is the vertex of the absolute value function below?

Question illustration
A
(4, –1)
B
(1, –4)
C
(1, 4)
D
(4, 1)
5

The graph of is transformed as shown in the graph below. Which equation represents the transformed function?

Question illustration
A
y = x cubed minus 4
Option A
B
y = (x minus 4) cubed
Option B
C
y = (negative x minus 4) cubed
Option C
D
y = (negative x) cubed minus 4
Option D
6

The standard diameter of a golf ball is 42.67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0.002 mm. Which function could represent this situation?

A
f(x ) = x – |42.67|
B
f(x ) = |x| – 42.67
C
f(x ) = |42.67 – x|
D
f(x ) = 42.67 – |x|
7

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
8

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}
9

If , what is f(5.9)?

Question illustration
A
9
B
10
C
11
D
12
10

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
11

What is the solution to the inequality ?

Question illustration
A
–3 > n > –2
B
2 < n < 3
C
n –2
D
n 3
12

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
13

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
14

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
15

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
16

How is the graph of transformed to produce the graph of ?

Question illustration
A
The graph is translated left 5 units, compressed vertically by a factor of , and translated up 3 units.
Option A
B
The graph is stretched vertically by a factor of , translated left 5 units, and translated up 3 units.
Option B
C
The graph is translated left 5 units, compressed horizontally by a factor of , and translated down 3 units.
Option C
D
The graph is stretched horizontally by a factor of , translated left 5 units, and translated down 3 units.
Option D
17

Jamilla solved the inequality and graphed the solution as shown below. What is the value of b and the missing symbol in Jamilla’s inequality?

Question illustration
A
b = –1,
Option A
B
b = –1,
Option B
C
b = 1,
Option C
D
b = 1,
Option D
18

Which statement is true about ?

Question illustration
A
The graph of f(x) has a vertex of (–4, 6).
B
The graph of f(x) is a horizontal stretch of the graph of the parent function.
C
The graph of f(x) opens upward.
D
The graph of f(x) has a domain of x –6.
Option D
19

A company manufactures 16-oz boxes of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0.15 oz, the production is stopped. What is the range of acceptable values for production to continue?

A
15.15 oz to 16.00 oz
B
15.85 oz to 16.00 oz
C
15.85 oz to 16.15 oz
D
16.15 oz to 16.45 oz
20

Based on the family the graph below belongs to, which equation could represent the graph?

Question illustration
A
y = StartFraction 1 Over x + 2 EndFraction + 3
Option A
B
y = 0.2 Superscript x Baseline + 3
Option B
C
y = x cubed + 3
Option C
D
y = log x + 3
Option D

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