Exploring Linear and Nonlinear Functions

This video tutorial explains how to identify linear and non-linear functions by examining tables. Linear functions have a constant rate of change and form straight lines on graphs, while non-linear functions do not. The tutorial provides examples to illustrate these concepts and guides students through practice exercises to identify function types based on changes in x and y values.

What is a key characteristic of a linear function when graphed?

• It has a variable rate of change.

• It forms a straight line.

• It cannot be graphed.

• It forms a curved line.

How can you determine if a function is non-linear by looking at its graph?

• The graph will have a constant rate of change.

• The graph will not form a straight line.

• The graph will form a straight line.

• The graph will be a single point.

In the first example, what is the rate of change in the y values?

• An increase of 2

• An increase of 15

• A constant rate of change

• A decrease of 15

Why is the function in the first example considered linear?

• Because the rate of change in y values is constant.

• Because the rate of change in x values is variable.

• Because the graph forms a curve.

• Because the y values decrease by different amounts.

In the second example, what is the rate of change in the x values?

• A constant rate of change

• An increase of 2

• A decrease of 15

• An increase of 3

Why is the function in the second example considered non-linear?

• Because the rate of change in y values is not constant.

• Because the rate of change in y values is constant.

• Because the rate of change in x values is variable.

• Because the graph forms a straight line.

In the task explanation, what is the rate of change in the x values for the linear function example?

• A decrease of 4

• An increase of 5

• A decrease of 15

• An increase of 2

What is the rate of change in the y values for the linear function example in the task explanation?

• A decrease of 15

• A decrease of 4

• An increase of 2

• An increase of 5

In the non-linear function example, what is the rate of change in the y values from 2 to 8?

• An increase of 10

• An increase of 2

• A decrease of 4

• An increase of 6

Why is the function in the non-linear example considered non-linear?

• Because the rate of change in y values is constant.

• Because the rate of change in x values is variable.

• Because the graph forms a straight line.

• Because the rate of change in y values is not constant.