Answers2026-2027_MDCPS_1200330_Algebra 2_FYComparing Characteristics of Functions

Comparing Characteristics of Functions — Unit test Answers

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

A
The ranges of both f(x) and g(x) are limited to y ≥ –1.
B
The ranges of both f(x) and g(x) are limited to y ≤ –1.
C
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.
D
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.
2
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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
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?

A
StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2nd Row 10 x + 4 y = 352 EndLayout
Option A
B
StartLayout Enlarged Left-Brace 1st Row 10 x + 4 y = 4,000 2nd Row x + y = 352 EndLayout
Option B
C
StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2ndRow 0.1 x + 0.04 y = 352 EndLayout
Option C
D
StartLayout Enlarged Left-Brace 1st Row 0.1 x + 0.04 y = 4,000 2nd Row x + y = 352 EndLayout
Option D
4

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.
5

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
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

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
8

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
9

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?

A
0.65 seconds
B
0.92 seconds
C
1.08 seconds
D
1.15 seconds
10

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
11

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
12

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
13

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
14

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
15

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.

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