Exploring Linear and Nonlinear Functions

This video tutorial covers the concepts of linear and nonlinear functions, explaining how to identify them based on their rate of change. It provides practical examples, such as ticket sales and square measurements, to illustrate these concepts. The tutorial also includes a section on graphing functions to visually determine their linearity.

What is a key characteristic of a linear function?

• Its graph is a curve.

• It has a variable rate of change.

• Its graph is a straight line.

• It has no rate of change.

How can you determine if a function is linear?

• By checking if the rate of change is constant.

• By checking if the function has no rate of change.

• By checking if the rate of change is variable.

• By checking if the function has multiple rates of change.

If the change in y-values is -5 and the change in x-values is 2, what is the rate of change?

• -2.5

• -7.5

• 2.5

• -5

Why is the function with y-values changing by +15, +33, and +50 considered nonlinear?

• Because the function has no rate of change.

• Because the rate of change is not constant.

• Because the y-values are not constant.

• Because the x-values are not constant.

What is the rate of change for a function where y-values change by -4 and x-values change by +5?

• -0.8

• 0.8

• -4

• 5

In the context of a tiger cub's calorie intake, why is the function considered nonlinear?

• Because the rate of change in calorie intake is not constant.

• Because the age in weeks is not constant.

• Because the calorie intake is not constant.

• Because the function has no rate of change.

If ticket sales for a school dance cost $5 per student, is this a linear function?

• No, because the ticket sales are constant.

• Yes, because the ticket sales are not constant.

• No, because the rate of change is variable.

• Yes, because the rate of change is constant.

Why is the area of a square with side lengths 1, 2, 3, 4, and 5 considered a nonlinear function?

• Because the side lengths are not constant.

• Because the area does not have a constant rate of change.

• Because the perimeter is not constant.

• Because the function has no rate of change.

What is the rate of change for the perimeter of a square with side lengths 1, 2, 3, 4, and 5?

• 3

• 4

• 1

• 2

What does it mean if the graph of a function is a straight line?

• The function is nonlinear.

• The function has a variable rate of change.

• The function has no rate of change.

• The function is linear.