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 can have curves or varying rates of change.

Front

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

Back

A linear function will have a constant difference between the y-values for equal increments in the x-values.

Front

What does the slope of a linear function represent?

Back

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

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 when graphed.

Front

How does the graph of a linear function differ from that of a nonlinear function?

Back

The graph of a linear function is a straight line, while the graph of a nonlinear function can be curved or have bends.

Front

What is a constant rate of change?

Back

A constant rate of change means that the change in y for each unit change in x is the same throughout the function.