Answers SS26 Math 3 S2 M3960OXStep Functions

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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?

$0.40

$2.50

$3.75

$4.00

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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

$7.40

$7.47

$7.53

$7.66

Which of the following describes the graph of ?

The graph has closed circles on the left of each step and open circles on the right and includes the step .

The graph has closed circles on the left of each step and open circles on the right and includes the step .

The graph has open circles on the left of each step and closed circles on the right and includes the step .

The graph has open circles on the left of each step and closed circles on the right and includes the step .

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.

37.1 m3

71.9 m3

116.5 m3

130.8 m3

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

Town B has the same population as Town A.

Town B has a greater population than Town A.

Town B has a population of approximately 5,138.

Town B has a population of approximately 37,530.

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.

21.1 cm3

23.6 cm3

27.6 cm3

31.6 cm3

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

square

trapezoid

triangle

non-square rectangle

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?

The residents of City A are more likely to use public buses because their city has a greater population density.

The residents of City B are more likely to use public buses because their city has a greater population density.

The residents of both cities are equally likely to use public buses because both population densities are about the same.

The residents of both cities are unlikely to use public buses because both population densities are too high.

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

square

trapezoid

triangle

non-square rectangle

A county in North Carolina spans 532 square miles. The population density of deer in the county is 11 deer per square mile.How many deer live in the county? Round to the nearest whole number, if necessary.

48 deer

68 deer

5,852 deer

5,992 deer

Which statement best compares the graphs of and ?

The two graphs are exactly the same.

The open and closed circles are reversed.

The graph of is shifted up compared to the graph of , and the open and closed circles are reversed.

The graph of is shifted up compared to the graph of , and the open and closed circles are the same.

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?

mc022-1.jpg

mc022-2.jpg

mc022-3.jpg

mc022-4.jpg

What is the range of the function graphed below?

mc022-2.jpg

mc022-3.jpg

mc022-4.jpg

mc022-5.jpg

Consider the functions.f(x) = (x + 1)2 – 4g(x) = –4 |x + 1|

The ranges of both f(x) and g(x) are limited to y ≥ –1.

The ranges of both f(x) and g(x) are limited to y ≤ –1.

Since the range of f(x) is limited to y ≤ 0 and the range of g(x) is limited to y ≥ –4, the ranges overlap for the values –4 ≤ y ≤ 0.

Since the range of f(x) is limited to y ≥ –4 and the range of g(x) is limited to y ≤ 0, the ranges overlap for the values –4 ≤ y ≤ 0.

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

point discontinuity at x = –2

point discontinuity at x = 4; jump discontinuity at x = –2

point discontinuities at x = –4 and x = 4; jump discontinuity at x = –2

jump discontinuities at x = –4, x = –2, and x = 4

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?

151

401

529

601

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

f(–2) = –6

f(–2) = –4

f(–2) = 0

f(–2) = 3

The graphs of three functions are shown.

All of the functions have a maximum.

The square root and quadratic function share a minimum.

The absolute value and quadratic function share a y-intercept.

The absolute value and square root function share an x-intercept.

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.

37.1 m3

71.9 m3

116.5 m3

130.8 m3

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

square

triangle

trapezoid

circle

non-square rectangle

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

Option

f(x) = (x + 3)2 – 2

Option

f(x) = –(x – 6)2 – 3

A store owner puts in an order for product X and product Y for a total of 4,000 units. It costs $0.10 per item to ship of product X and $0.04 per item to ship product Y. If the total shipping cost is $352, which system of equations can be used to determine how much of product X and product Y the store owner bought?

StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2nd Row 10 x + 4 y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row 10 x + 4 y = 4,000 2nd Row x + y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2ndRow 0.1 x + 0.04 y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row 0.1 x + 0.04 y = 4,000 2nd Row x + y = 352 EndLayout

A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10 units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units.

(14)(10)(8) – π(2.52)(8)

(14)(10)(8) + π(2.52)(8)

(10)(8)(14) – π(2.52)(8)

(10)(8)(14) + π(2.52)(8)

151

401

529

601

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

g(x) has the lowest minimum.

f(x) has the greatest maximum.

All three functions have a y-intercept.

All three functions have an x-intercept.

The domain of all three functions is the same.

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Sharon jumps, Megan throws a beach ball up to Sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?

0.65 seconds

0.92 seconds

1.08 seconds

1.15 seconds

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 horizontal segment with an open circle at (20, 10) and a closed circle at (30, 10); $207.50

a horizontal segment with a closed circle at (20, 10) and an open circle at (30, 10); $207.50

a horizontal segment with an open circle at (21, 10) and a closed circle at (30, 10); $311.25

a horizontal segment with a closed circle at (21, 10) and an open circle at (30, 10); $311.25

Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet.Which statement is true regarding the areas of the two flower beds?

Henry’s design would result in a larger flower bed because its area would be 2,500 square feet.

Liani’s design would result in a larger flower bed because its area would be 2,500 square feet.

Henry’s and Liani’s designs would result in flower beds with the same area.

Henry’s and Liani’s designs are not possible with the given amount of wood.

Which of the following describes the graph of ?

The graph has closed circles on the left of each step and open circles on the right and includes the step .

The graph has open circles on the left of each step and closed circles on the right and includes the step .

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.

1,200 units3

4,400 units3

5,040 units3

6,000 units3

0.65 seconds

0.92 seconds

1.08 seconds

1.15 seconds

Which statement best compares the graphs of and ?

The two graphs are exactly the same.

The open and closed circles are reversed.

The graph of is shifted up compared to the graph of , and the open and closed circles are reversed.

The graph of is shifted up compared to the graph of , and the open and closed circles are the same.

square

triangle

trapezoid

circle

non-square rectangle

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

Town B has the same population as Town A.

Town B has a greater population than Town A.

Town B has a population of approximately 5,138.

Town B has a population of approximately 37,530.

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