Linear vs. Nonlinear Functions

What is the rate of change of the function?

-2

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)?

-5

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

0

Look at the graph of the linear function. mc004-1.jpg The rate of change between point A and point B is 2. What is the rate of change between point C and point D?

2

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

2.5

Which graph has a rate of change of zero?

B

Which of these tables represents a linear function?

B

Which of these tables represents a non-linear function?

C

Which graph represents a function with a rate of change of 0.5?

D

Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the differences in the y-values as 7 - 1 = 6, 17 - 7 = 10, and 31 - 17 = 14. Then he concluded that since the differences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is linear. What was Willis's mistake?

He concluded that the function has a constant rate of change.

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

It is linear because it has a constant rate of change.

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

It is not linear because it does not have a constant rate of change.

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?

It represents a non-linear function because there is not a constant rate of change.

Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change?

3/16

Is the function represented by the table linear?

No, because it does not have a constant rate of change.

Look at the graph. mc009-1.jpg To find the rate of change of the function, Kevin did the following: What was Kevin's mistake?

He mixed up the numerator and the denominator of the fraction.

Look at the graph. mc017-1.jpg 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 mc017-2.jpg and the rate of change between the points (0, -3) and (2, 5) to be mc017-3.jpg. Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong?

Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.