3.2 Linear vs. Nonlinear

Front

What is the difference between discrete and continuous graphs?

Back

Discrete graphs consist of distinct points, while continuous graphs are unbroken and can take any value within a range.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Front

What defines a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What defines a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line, often represented by equations that include exponents, roots, or other non-linear operations.

Tags

CCSS.8.F.A.3

Front

What is an example of a linear function in real life?

Back

The distance traveled by a car at a constant speed over time is a linear function.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is an example of a nonlinear function in real life?

Back

The amount of snow on the ground after several days of spring, which may not increase at a constant rate.

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function will have a curve or bend in its graph, rather than being a straight line.

Tags

CCSS.8.F.A.3

Front

What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of y with respect to x.

Tags

CCSS.8.EE.B.5

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as x increases, y also increases.

Front

What does it mean if a function is decreasing?

Back

A function is decreasing if, as x increases, y decreases.

Front

What is a vertical line in terms of function classification?

Back

A vertical line represents a nonlinear function because it does not pass the vertical line test.