Linear vs. Nonlinear Tables and Graphs

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

Front

How can you determine if a table of values represents a linear function?

Back

A table represents a linear function if the differences between consecutive y-values divided by the differences between consecutive x-values (the rate of change) are constant.

Front

What does the slope of a line represent in a linear function?

Back

The slope of a line represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is zero.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How can you identify a nonlinear graph?

Back

A nonlinear graph can be identified by its curved shape, which indicates that the rate of change is not constant.

Front

What is the difference between a steep and a gentle slope?

Back

A steep slope indicates a large change in y for a small change in x, while a gentle slope indicates a small change in y for a larger change in x.

Front

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

Back

A function has a constant rate of change if the change in the output (y) is proportional to the change in the input (x) across the entire domain.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is a quadratic function, such as y = x^2, which produces a parabolic graph.