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Linear vs. Nonlinear Functions Answers

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Jamal drew the function below. Which explains whether or not his function is linear?

Question illustration
A
It is linear because it has a constant rate of change.
B
It is linear because it does not have a constant rate of change.
C
It is not linear because it has a constant rate of change.
D
It is not linear because it does not have a constant rate of change.
2
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Which graph has a rate of change of zero?

A
On a coordinate plane, a vertical line is at x = 3.
Option A
B
On a coordinate plane, a horizontal line is at y = 3.
Option B
C
On a coordinate plane, a line with positive slope goes through (0, 0) and (1, 3).
Option C
D
On a coordinate plane, a line with negative slope goes through (negative 1, 3) and (0, 0).
Option D
3

Is the function represented by the table linear?xy10–61111261312

A
Yes, because it has a constant rate of change.
B
Yes, because it does not have a constant rate of change.
C
No, because it has a constant rate of change.
D
No, because it does not have a constant rate of change.
4

Look at the graph of the linear function. The rate of change between point A and point B is 2. What is the rate of change between point C and point D?

Question illustration
A
–2
B
Negative one-half
Option B
C
One-half
Option C
D
2
5

Is the function represented by the table non-linear?xy6472809–2

A
Yes, because it has a constant rate of change.
B
Yes, because it does not have a constant rate of change.
C
No, because it has a constant rate of change.
D
No, because it does not have a constant rate of change.
6

Juno is taking a taxi. The table represents a linear function and shows the amount she owed after various numbers of miles traveled. Is the rate of change 2.25?Amount Juno Owed for a TaxiMilesAmount Owed (dollars)12.524.753749.25511.5

A
Yes, because the amount owed changes by 1 every time the miles change by 2.25.
B
Yes, because the amount owed changes by 2.25 every time the miles change by 1.
C
No, because the amount owed does not change by 1 every time the miles change by 2.25.
D
No, because the amount owed does not change by 2.25 every time the miles change by 1.
7

The table below represents the number of math problems Jana completed as a function of the number of minutes since she began doing her homework. Does this situation represent a linear or non-linear function, and why?Jana’s Math Homework ProgressMinutesMath Problems Completed1327312416519

A
It represents a linear function because there is a constant rate of change.
B
It represents a linear function because there is not a constant rate of change.
C
It represents a non-linear function because there is a constant rate of change.
D
It represents a non-linear function because there is not a constant rate of change.
8

Max is painting a fence.The table shows the number of square feet he painted after various numbers of minutes. What is the rate of change?Amount of Fence Max PaintedMinutesSquare Feet Painted13.527310.5414517.5

A
–3.5
B
–1
C
1
D
3.5
9

Jordana drew the function below. Which statement correctly explains whether or not her function is linear?

Question illustration
A
It is linear because it has a constant rate of change.
B
It is linear because it does not have a constant rate of change.
C
It is not linear because it has a constant rate of change.
D
It is not linear because it does not have a constant rate of change.
10

Which of these tables represents a linear function?

A
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries 3, 4, 6, 7.
Option A
B
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries 6, 5, 4, 3.
Option B
C
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries 7, 6, 5, 3.
Option C
D
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries 2, 4, 5, 6.
Option D
11

What is the rate of change of the function?

Question illustration
A
–2
B
Negative one-half
Option B
C
One-half
Option C
D
2
12

Which of these tables represents a non-linear function?

A
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries 20, 19, 18, 17.
Option A
B
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries negative 16, negative 17, negative 18, negative 19.
Option B
C
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries 16, 17, 19, 20.
Option C
D
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries negative 20, negative 19, negative 18, negative 17.
Option D
13

What is the rate of change of the function represented by the table?xy1–8.52–63–3.54–1

A
–2.5
B
–1
C
1
D
2.5
14

The table represents a linear function. The rate of change between the points (–5, 10) and (–4, 5) is –5. What is the rate of change between the points (–3, 0) and (–2, –5)?xy–510–45–30–2–5

A
–5
B
Negative StartFraction 1 Over 5 EndFraction
Option B
C
One-fifth
Option C
D
5
15

Look at the graph. To find the rate of change of the function, Kevin did the following: What was Kevin’s mistake?

Question illustration
A
He incorrectly chose (4,0) as a point on the graph.
B
He incorrectly chose (0, 2) as a point on the graph.
C
He mixed up the numerator and the denominator of the fraction.
D
He subtracted –2 from 0 when he should have added –2 to 0.

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