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 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 ratio of the change in y to the change in x.

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).

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

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

Back

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

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 graphs to a parabola.

Front

How can you tell if a function is nonlinear from its graph?

Back

If the graph is curved or does not form a straight line, the function is nonlinear.