Identifying Linear and Nonlinear Functions

The video tutorial explains how to determine if a function is linear or nonlinear. A linear function is characterized by a straight line or a constant rate of change, while a nonlinear function has a curve and lacks a constant rate of change. The video provides examples to illustrate these concepts, showing how to analyze functions visually and through their rate of change. It covers four examples, two linear and two nonlinear, demonstrating how to identify the characteristics of each type of function.

What is a key characteristic of a linear function?

• It does not intersect the y-axis.

• It forms a curve on a graph.

• It has a constant rate of change.

• It has varying rates of change.

How can you visually identify a nonlinear function?

• It passes through the origin.

• It forms a straight line.

• It has a constant slope.

• It forms a curve.

In Example 1, what indicates that the function is nonlinear?

• The function has a constant rate of change.

• The function is a straight line.

• The function starts at zero.

• The function forms a curve.

What is the rate of change in Example 2?

• 1:4

• 4:1

• 2:1

• 1:1

In Example 2, why is the function considered linear?

• It has a varying rate of change.

• It forms a curve.

• It has a constant rate of change.

• It does not pass through the origin.

How do you determine if a function is linear in Example 3?

• By checking if the graph is a curve.

• By calculating if the rates of change are constant.

• By seeing if it passes through the origin.

• By checking if it has a negative slope.

What is the rate of change calculated in Example 3?

• 1:1

• 3:1

• 4:1

• 2:1

In Example 4, what indicates the function is nonlinear?

• The rates of change are constant.

• The rates of change vary.

• The function forms a straight line.

• The function passes through the origin.

What is the issue with the rates of change in Example 4?

• They are all zero.

• They vary between positive and negative.

• They are all negative.

• They are all positive.

How can you determine if a function is linear or nonlinear?

• By seeing if it passes through the origin.

• By checking if it has a positive slope.

• By calculating the rate of change.

• By checking if it forms a curve.