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 has 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 between the y-values for equal increments in the x-values.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the rate of change, representing how much y changes for a unit change in x.

Front

What does it mean if a function has a constant rate of change?

Back

It means that for every equal increase in x, the increase in y is always the same, indicating a linear relationship.

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

Can a linear function have a curved graph?

Back

No, a linear function cannot have a curved graph; if the graph is curved, it is a nonlinear function.

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

Back

A linear equation can be written in the form y = mx + b, while a nonlinear equation cannot be expressed in this form.

Front

How do you determine if a function is linear or nonlinear from its equation?

Back

If the equation can be simplified to the form y = mx + b, it is linear; otherwise, it is nonlinear.