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 and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. It has a variable rate of change and can include curves, bends, or other shapes.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from a table of values?

Back

A linear function can be identified from a table of values if the ratio of the change in the y-values to the change in the x-values is constant.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function, indicating how much the y-value changes for a unit change in the x-value.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the general form of a linear equation?

Back

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

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.

Tags

CCSS.8.F.A.3

Front

How can you tell if a graph represents a linear function?

Back

A graph represents a linear function if it forms a straight line without any curves or bends.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

A linear graph is a straight line, while a nonlinear graph can be curved or have varying slopes.

Tags

CCSS.8.F.A.3

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 y-value is consistent for each unit change in the x-value.

Tags

CCSS.HSF-LE.A.1B