Linear vs. Nonlinear

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. It may have curves or bends.

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 the y-values divided by the difference in the x-values is the same for any two points on the line.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope.

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function can be identified by its curved or bent graph, which does not have a constant slope.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the rise (change in y) to the run (change in x) between any two points on the line.

Front

What is the y-intercept of a linear function?

Back

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

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means the line decreases as it moves from left to right.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which creates a parabolic curve when graphed.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3, which creates a straight line when graphed.