AnswersVA-Mathematical AnalysisStep Functions

Step Functions — Unit test Answers

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Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. If the prices are the same at both concession stands, what is the price of a hot dog?

A
$0.40
B
$2.50
C
$3.75
D
$4.00
2
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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
3

The table shows information about Town A in Illinois and Town B in Florida.

Question illustration
A
Town B has the same population as Town A.
B
Town B has a greater population than Town A.
C
Town B has a population of approximately 5,138.
D
Town B has a population of approximately 37,530.
4

The more people living in an area, the more likely it is that public buses will be used. City A has a population of 51,242 and covers an area of 89.22 mi2. City B has a population of 50,178 and covers an area of 8.12 mi2.Which statement about use of public buses in the cities is most likely true?

A
The residents of City A are more likely to use public buses because their city has a greater population density.
B
The residents of City B are more likely to use public buses because their city has a greater population density.
C
The residents of both cities are equally likely to use public buses because both population densities are about the same.
D
The residents of both cities are unlikely to use public buses because both population densities are too high.
5

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
6

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
7

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
8

The graphs of three functions are shown.

Question illustration
A
All of the functions have a maximum.
B
The square root and quadratic function share a minimum.
C
The absolute value and quadratic function share a y-intercept.
D
The absolute value and square root function share an x-intercept.
9

Which function has the same maximum value as f(x) = – |x + 3| – 2?

A
Option
Option A
B
f(x) = (x + 3)2 – 2
C
Option
Option C
D
f(x) = –(x – 6)2 – 3
10

A company plans to sell embroidered hats for $15 each. The company’s financial planner estimates that the cost, y, of manufacturing the hats is a quadratic function with a y-intercept of 7,920 and a vertex of (150, 9,000). What is the minimum number of hats the company must sell to make a profit?

A
151
B
401
C
529
D
601
11

Which statements can be used to accurately compare the functions? Select two options.

A
g(x) has the lowest minimum.
B
f(x) has the greatest maximum.
C
All three functions have a y-intercept.
D
All three functions have an x-intercept.
E
The domain of all three functions is the same.
12

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
13

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
14

A triangular prism with a rectangular base is stacked on top of a rectangular prism. The rectangle has side lengths of 20 and 15 units. The rectangular prism has a height of 12. The triangular prism has a height of 16 units.

Question illustration
A
1,200 units3
B
4,400 units3
C
5,040 units3
D
6,000 units3
15

A cross section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base.The cross section can be which of these shapes? Select three options.squaretriangletrapezoidcirclenon-square rectangle

A
square
B
triangle
C
trapezoid
D
circle
E
non-square rectangle
16

A manager needs to order company shirts for each employee. She was quoted the following rates. If she orders 75 shirts and passes the cost along to the employees, what would each employee owe for the shirt if each pays the same amount? Round to the nearest cent. Price Quote for Company Work ShirtsNumber of shirts orderedCost per shirtFirst 19 shirts$10Next 30 shirts$8Each shirt over 49$5

A
$7.40
B
$7.47
C
$7.53
D
$7.66
17

A grain silo is composed of a cylinder and a hemisphere. The diameter is 4.4 meters. The height of its cylindrical portion is 6.2 meters.

Question illustration
A
37.1 m3
B
71.9 m3
C
116.5 m3
D
130.8 m3
18

A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. The apothem of the hexagon is 2 centimeters.

Question illustration
A
21.1 cm3
B
23.6 cm3
C
27.6 cm3
D
31.6 cm3
19

A polygon with 3 sides is stacked to form a prism.

Question illustration
A
square
B
trapezoid
C
triangle
D
non-square rectangle
20

A polygon with 3 sides is stacked to form a prism.

Question illustration
A
square
B
trapezoid
C
triangle
D
non-square rectangle

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