8.AF.4 Describing Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values increase, the output values decrease.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line 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 graph to a straight line and can include curves, parabolas, and other shapes.

Front

What is a proportional relationship?

Back

A proportional relationship is one where the ratio of the two quantities is constant, meaning that as one quantity increases, the other increases at a consistent rate.

Front

What is a nonproportional relationship?

Back

A nonproportional relationship is one where the ratio of the two quantities is not constant, meaning that the relationship does not maintain a consistent rate of change.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified by a straight line on a graph, indicating a constant rate of change.

Front

How can you identify a nonlinear function from a graph?

Back

A nonlinear function can be identified by a curve or any shape that is not a straight line on a graph.

Front

What is the difference between a linear and a nonlinear equation?

Back

A linear equation has a degree of 1 and graphs to a straight line, while a nonlinear equation has a degree greater than 1 and graphs to a curve.