Linear VS Nonlinear Functions

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 has a variable rate of change.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by a straight line graph.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation 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 does the y-intercept of a linear function represent?

Back

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

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, indicating that as x increases, y decreases.

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.

Front

What is the difference between a linear and a nonlinear equation?

Back

A linear equation has a constant rate of change and graphs as a straight line, while a nonlinear equation has a variable rate of change and graphs as a curve.

Front

How do you determine if a function is linear or nonlinear from a table of values?

Back

If the differences between consecutive y-values are constant for equal x-intervals, the function is linear; if not, it is nonlinear.