Linear vs. Nonlinear

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and does not have a constant 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 of x-values.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x, representing the rate of change.

Front

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

Back

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

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3.

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^2.

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.

Front

How can you tell if a function is nonlinear by its equation?

Back

If the equation includes variables raised to a power other than one, or includes products of variables, it is nonlinear.

Front

What is a common characteristic of nonlinear functions?

Back

Nonlinear functions can have curves, bends, or changes in direction.