3.2 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 can have curves or bends.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by a straight line on the graph.

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 the input (x), the output (y) increases by a fixed amount.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope in a linear function?

Back

The slope (m) represents the steepness of the line and the direction of the change in y with respect to x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b).

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means the line goes down as it moves from left to right.

Front

What is an example of a nonlinear function?

Back

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

Front

How do you determine if a function is linear or nonlinear from a table of values?

Back

If the differences between consecutive y-values are constant for equal x-intervals, the function is linear; otherwise, it is nonlinear.