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Comparing Characteristics of Functions Answers

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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.
2
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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
3

Which functions have a y-intercept that is greater than the y-intercept of the function g(x) = |x + 3| + 4? Check three options.f(x) = –2 (x – 8)2h(x) = –5 |x| + 10j(x) = –4(x + 2)2 + 8

Question illustration
A
f(x) = –2 (x – 8)2
B
h(x) = –5 |x| + 10
C
j(x) = –4(x + 2)2 + 8
D
Option
Option D
E
Option
Option E
4

Which function has the greatest maximum range value?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

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.
6

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.
7

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.
8

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).
9

Two different functions are represented.

Question illustration
A
Neither function A nor function B has an x-intercept.
B
Neither function A nor function B has a y-intercept.
C
The domain and range of both functions contain only positive numbers.
D
The domain and range of both functions contain only positive numbers and zero.
10

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.
11

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
12

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.
13

Which statements accurately compare the functions on the graph? Select two options.

A
The square root and quadratic function share a y-intercept.
B
The square root and absolute value function share an x-intercept.
C
The range of the square root and quadratic function are the same.
D
The range of the square root and absolute value function are the same.
E
The quadratic function and the absolute value function have a minimum while the square root function has a maximum.
14

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.
15

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

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