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Linear vs. Nonlinear Functions Answers

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Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change?Distance Carol Traveled while Cross-Country SkiingMinutesDistance Traveled (miles)23456

Question illustration
A
StartFraction 1 Over 12 EndFraction
Option A
B
StartFraction 1 Over 6 Endfraction
Option B
C
StartFraction 3 Over 32 EndFraction
Option C
D
StartFraction 3 Over 16 EndFraction
Option D
2
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Look at the graph. Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be (–1, –4), (0, -3), and (2, 5). Next, she determined the rate of change between the points (–1, –4) and (0, -3) to be and the rate of change between the points (0, -3) and (2, 5) to be . Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong?

Question illustration
A
The points (–1, –4), (0, –3), and (2, 5) are not all on the graph.
B
The expressions and both equal 1.
Option B
C
She miscalculated the rates of change.
D
Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.
3

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.
4

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
5

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.
6

What is the rate of change of the function represented by the table?xy15253545

A
0
B
1
C
4
D
5
7

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.
8

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.
9

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
10

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

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