Answers2026-2027_MDCPS_1200330_Algebra 2_FYComparing Characteristics of Functions

Comparing Characteristics of Functions — Unit test Answers

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The graph shows the exponential regression model for data representing a rabbit population after x years.

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A
The graph of the regression model is limited to whole-number values for x.
B
The graph of the regression model is limited to whole-number values for y.
C
The graph of the regression model cannot be used to approximate the population size for year 1.
D
The graph of the regression model can be used to predict the population size for any number of years in the future.
2
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Fuaad solved an absolute value inequality and expressed the solution as . What is another way to show Fuaad’s solution?

Question illustration
A
Option
Option A
B
(–12, 7]
C
Option
Option C
D
Option
Option D
3

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 negative infinity. To which family of functions might the described function belong?

A
absolute value
B
exponential
C
cube root
D
square root
4

Which graph represents an even function?

A
A coordinate plane has 5 points. The points are (negative 6, negative 4), (negative 4, 2), (2, 4), (4, negative 2), (6, 2).
Option A
B
A coordinate plane has 7 points. The points are (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6).
Option B
C
A coordinate plane has 7 points. The points are (negative 5, 2), (negative 4, 1), (negative 3, 3), (negative 2, 5), (2, negative 2), (3, negative 5), (4, negative 6).
Option C
D
A coordinate plane has 7 points. The points are (negative 4, negative 3), (negative 3, negative 5), (negative 2, 1), (0, 0), (2, 1), (3, negative 5), (4, negative 3).
Option D
5

If the function has an inverse function, which statement must be true?

Question illustration
A
b not-equals 0
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

Which of the following is an odd function?

A
g(x) = x2
B
g(x) = 5x – 1
C
g(x) = 3
D
g(x) = 4x
7

Which statement best describes how to determine whether f(x) = x2 – x + 8 is an even function?

A
Determine whether –x2 – (–x) + 8 is equivalent to x2 – x + 8.
B
Determine whether (–x)2 – (–x) + 8 is equivalent to x2 – x + 8.
C
Determine whether –x2 – (–x) + 8 is equivalent to –(x2 – x + 8).
D
Determine whether (–x)2 – (–x) + 8 is equivalent to –(x2 – x + 8).
8

The table below shows the different times it takes Paula to drive to her grandmother’s house depending on the rate at which she drives.Rate vs. TimeRate (mph)30405060Time (h)2.51.8751.51.25If one day Paula rides a scooter to her grandmother’s house at a constant rate of 24 miles per hour, how long should it take her?

A
2.625 hours
B
2.75 hours
C
3.125 hours
D
3.75 hours
9

Over which interval are the exponential and linear function approximately the same?

Question illustration
A
from 0.25 to 0.5
B
from 0.5 to 0.75
C
from 0.75 to 1.0
D
from 1.25 to 1.5
10

Which of the following best describes how the y values are changing over each interval?xy122438416532

A
They are increasing by 2 each time.
B
They are increasing by 4 each time.
C
They are being multiplied by 2 each time.
D
They are being multiplied by 4 each time.
11

Adita has two options for how to invest $1,000.Plan A: Put the $1,000 in an account that pays $100 per year.Plan B: Put the $1,000 in an account that pays 5 percent interest per year.Which statement is true?

A
Plan A will be worth more than plan B after two years.
B
Plan A will be worth the same amount as plan B after one year.
C
Plan B will be worth more than plan A after three years.
D
Plan B will be worth more than plan A after four years.
12

For which pair of functions is ?

Question illustration
A
f(x) = 3 – 4x and g(x) = 16x – 3
B
f(x) = 6x2 and
Option B
C
and g(x) = 144x
Option C
D
f(x) = 4x and g(x) = 3x
13

The tables for f(x) and g(x) are shown below.xf(x)–5–11–21113529xg(x)–5–7–2–115513What is the value of (f – g)(5)?

A
–18
B
–4
C
16
D
42
14

The table shows the approximate height of an object x seconds after the object was dropped. The function h(x) = –16x2 + 100 models the data in the table.

Question illustration
A
–2.75
B
0.25
C
1.75
D
2.25
15

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
16

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
17

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.
18

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.
19

The graph below is an example of which type of function?

Question illustration
A
quadratic
B
linear
C
cubic
D
square root
20

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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