8.F.3 Review - Linear vs. Nonlinear

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and does not have a constant rate of change.

Front

Identify the general form of a linear function.

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, b).

Front

How can you determine if a function is linear from its equation?

Back

If the equation can be written in the form y = mx + b, it is linear. If it includes variables raised to powers other than 1, it is nonlinear.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2.

Front

What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the difference in y-values divided by the difference in x-values is the same for any two points on the line.

Front

Why is the function y = 3x + 4 considered linear?

Back

It is considered linear because it can be expressed in the form y = mx + b, where m = 3 and b = 4.