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

If the differences between consecutive y-values are constant for equal intervals of x, the function is linear.

Front

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

Back

A constant rate of change means that for every unit increase in x, the change in y is always the same.

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 is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

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 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 as a parabola.

Front

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

Back

If the graph is a straight line, the function is linear; if it curves or bends, it is nonlinear.