AnswersVA-Mathematical AnalysisStep Functions

Step Functions — Unit test Answers

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1
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Given the function f(x) = –5|x + 1| + 3, for what values of x is f(x) = –12?

A
x = –2, x = –4
B
x = –2, x = 4
C
x = 2, x = –4
D
x = 2, x = 4
2
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Which is the graph of reflected across the x-axis, translated 3 units left, 4 units up, and dilated by a factor of 4?

Question illustration
A
mc026-2.jpg
Option A
B
mc026-3.jpg
Option B
C
mc026-4.jpg
Option C
D
mc026-5.jpg
Option D
3

Which statement is true about ?

Question illustration
A
The graph of f(x) has a vertex of (–3, 2).
B
The graph of f(x) is a horizontal compression of the graph of the parent function.
C
The graph of f(x) opens downward.
D
The graph of f(x) has range of f(x) –2.
Option D
4

Which of the following describes the graph of ?

Question illustration
A
The graph has closed circles on the left of each step and open circles on the right and includes the step .
Option A
B
The graph has closed circles on the left of each step and open circles on the right and includes the step .
Option B
C
The graph has open circles on the left of each step and closed circles on the right and includes the step .
Option C
D
The graph has open circles on the left of each step and closed circles on the right and includes the step .
Option D
5

What is the range of the function graphed below?

Question illustration
A
mc022-2.jpg
Option A
B
mc022-3.jpg
Option B
C
mc022-4.jpg
Option C
D
mc022-5.jpg
Option D
6

Which of the following accurately lists all discontinuities of the function below?

Question illustration
A
point discontinuity at x = –2
B
point discontinuity at x = 4; jump discontinuity at x = –2
C
point discontinuities at x = –4 and x = 4; jump discontinuity at x = –2
D
jump discontinuities at x = –4, x = –2, and x = 4
7

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

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

An international calling plan charges 45 cents per minute or fraction of a minute for each call. Which graph models the cost, y, in cents of making x minutes of international calls?

A
mc022-1.jpg
Option A
B
mc022-2.jpg
Option B
C
mc022-3.jpg
Option C
D
mc022-4.jpg
Option D
9

A farmer sells almonds according to the chart below. The more pounds of almonds that are sold, the lower the cost per pound is for the entire order of almonds.Almond PricesNumber of PoundsCost (per Pound)up to 10$20 more than 10, and up to 20$15 more than 20, and up to 30$10 more than 30$5 The farmer graphs a step function to model the situation, where y represents the cost per pound for an order of x pounds of almonds. Which of the following describes the farmer’s graph for the step that includes 20.75 pounds, and what is the total cost of 20.75 pounds of almonds?

A
a horizontal segment with an open circle at (20, 10) and a closed circle at (30, 10); $207.50
B
a horizontal segment with a closed circle at (20, 10) and an open circle at (30, 10); $207.50
C
a horizontal segment with an open circle at (21, 10) and a closed circle at (30, 10); $311.25
D
a horizontal segment with a closed circle at (21, 10) and an open circle at (30, 10); $311.25
10

Which statement best compares the graphs of and ?

Question illustration
A
The two graphs are exactly the same.
B
The open and closed circles are reversed.
C
The graph of is shifted up compared to the graph of , and the open and closed circles are reversed.
Option C
D
The graph of is shifted up compared to the graph of , and the open and closed circles are the same.
Option D
11

The equation of the piecewise function f(x) is below. What is the value of f(–2)?

Question illustration
A
f(–2) = –6
B
f(–2) = –4
C
f(–2) = 0
D
f(–2) = 3
12

Which graph shows the solution to the inequality ?

Question illustration
A
mc013-2.jpg
Option A
B
mc013-3.jpg
Option B
C
mc013-4.jpg
Option C
D
mc013-5.jpg
Option D
13

Which of the following is the graph of f(x) = 3|x – 4| + 1?

A
mc017-1.jpg
Option A
B
mc017-2.jpg
Option B
C
mc017-3.jpg
Option C
D
mc017-4.jpg
Option D
14

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

Question illustration
T
The graph is stretched horizontally by a factor of 2 and then moved right 4 units.
T
The graph is compressed horizontally by a factor of 2 and then moved down 4 units.
T
The graph is compressed horizontally by a factor of 2, moved left 4 units, and moved down 4 units.
T
The graph is stretched horizontally by a factor of 2, moved left 4 units, and moved down 4 units.
15

What is the solution, if any, to the inequality ?

Question illustration
A
no solution
B
all real numbers
C
n > 2 or n < 6
D
2 < n < 6

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