Linear vs Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that has a constant rate of change, represented by a straight line on a graph.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not have a constant rate of change, resulting in a curved line on a graph.

Front

How can you identify a linear function from a table of values?

Back

If the differences between consecutive y-values are constant for equal intervals of x, the function is linear.

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 linear function?

Back

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

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

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

How do you determine if a graph is linear or nonlinear?

Back

If the graph is a straight line, it is linear; if it curves, it is nonlinear.

Front

What is the significance of a constant rate of change in a linear function?

Back

A constant rate of change means that the function increases or decreases at the same rate throughout its domain.