Answers2026-2027_MDCPS_1200330_Algebra 2_FYComparing Characteristics of Functions

Comparing Characteristics of Functions Answers

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1
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Consider the functions.

Question illustration
A
The minimums of g(x) and h(x) are both in the first quadrant.
B
The minimums of g(x) and h(x) are both in the third quadrant.
C
The minimum of h(x) is farther right and up from the minimums of f(x) and g(x).
D
The minimum of h(x) is farther left and down from the minimums of f(x) and g(x).
2
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Which statements comparing the functions are true? Select three options.

A
Only f(x) and h(x) have y-intercepts.
B
Only f(x) and h(x) have x-intercepts.
C
The minimum of h(x) is less than the other minimums.
D
The range of h(x) has more values than the other ranges.
E
The maximum of g(x) is greater than the other maximums.
3

Which function has the greatest x-intercept?

A
f(x) = 3x – 9
B
g(x) = |x + 3|
C
h(x) = 2x – 16
D
j(x) = –5(x – 2)2
4

Two different functions are shown.Function A:Function B:

Question illustration
A
The x-intercept in function B is one-third as large as the x-intercept in function A.
B
The x-intercept in function B is three times as large as the x-intercept in function A.
C
The distance between the x-intercepts in function A is half the distance between the x-intercepts of function B.
D
The distance between the x-intercepts in function A is twice the distance between the x-intercepts of function B.
5

Question text not available

Answer not available
6

Which characteristics do the functions have in common? Select three options.

A
range
B
domain
C
maximum
D
x-intercept
E
y-intercept
7

The tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days.

Question illustration
A
Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
B
Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
C
Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.
D
Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.
8

Which function has a domain and range that includes all real values?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

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

A
f(x) has an all negative domain.
B
g(x) has the greatest maximum value.
C
All three functions share the same range.
D
h(x) has a range of all negative numbers.
E
All three functions share the same domain.
10

The tables show linear functions representing the estimated time it takes for the math and language arts portions of standardized tests with different numbers of questions.

Question illustration
A
The math function has the greater slope, which shows that the estimated time per question for math is less than the estimated time per question for language arts.
B
The math function has the greater slope, which shows that the estimated time per question for math is greater than the estimated time per question for language arts.
C
The language arts function has the greater slope, which shows that the estimated time per question for language arts is less than the estimated time per question for math.
D
The language arts function has the greater slope, which shows that the estimated time per question for language arts is greater than the estimated time per question for math.
11

Which function has exactly one x- and y-intercept?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

Which characteristics do the functions have in common? Select three options.

A
range
B
domain
C
maximum
D
x-intercept
E
y-intercept
13

Consider the functions.

Question illustration
A
The minimums of g(x) and h(x) are both in the first quadrant.
B
The minimums of g(x) and h(x) are both in the third quadrant.
C
The minimum of h(x) is farther right and up from the minimums of f(x) and g(x).
D
The minimum of h(x) is farther left and down from the minimums of f(x) and g(x).
14

Which function has a domain and range that includes all real values?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

Which statements comparing the functions are true? Select three options.

A
Only f(x) and h(x) have y-intercepts.
B
Only f(x) and h(x) have x-intercepts.
C
The minimum of h(x) is less than the other minimums.
D
The range of h(x) has more values than the other ranges.
E
The maximum of g(x) is greater than the other maximums.
16

Which function has the greatest x-intercept?

A
f(x) = 3x – 9
B
g(x) = |x + 3|
C
h(x) = 2x – 16
D
j(x) = –5(x – 2)2
17

Which function has a range limited to only negative numbers?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
18

Two different functions are shown.Function A:Function B: y = (x + 3)2 + 5

Question illustration
A
The minimum of function A occurs 1 unit higher than the minimum of function B.
B
The minimum of function A occurs 3 units higher than the minimum of function B.
C
The minimum of function A occurs 5 units lower than the minimum of function B.
D
The minimum of function A occurs 7 units lower than the minimum of function B.
19

Employees at a manufacturing plant have seen production rates change by approximately 105% annually. In contrast, the graph shows the change in the average annual wages of the employees.

Question illustration
A
The annual changes cannot be compared because the initial production value is unknown.
B
The annual change in production has exceeded the annual change in the average salary.
C
The annual change in production increases at a slower rate, 5% per year, than the annual increase in the average salary, $500 per year.
D
The annual change in production increases at a slower rate, 105% per year, than the annual increase in average salary, $500 per year.
20

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

A
Only f(x) has an x-intercept.
B
g(x) has the greatest maximum.
C
All three functions have a y-intercept.
D
All three functions have the same range values.
E
All three functions have the same domain values.

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