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 may have a variable rate of change.

Front

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

Back

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

Front

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

Back

It means that for every unit increase in the x-value, the y-value increases by a fixed amount.

Front

What is the slope of a linear function?

Back

The slope is the ratio of the change in y to the change in x, representing the steepness of the line.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

Can a function be both linear and nonlinear?

Back

No, a function is either linear or nonlinear, not both.

Front

What is an example of a nonlinear function?

Back

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

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value).

Front

How can you tell if a table of values represents a function?

Back

A table represents a function if no x-value is repeated with different y-values.