Linearity and Continuity of Graphs

Front

What is a linear function?

Back

A linear function is a function that can be graphed as a straight line. It has the form f(x) = 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 form a straight line when graphed. Its graph can be a curve or any other shape that is not a straight line.

Tags

CCSS.8.F.A.3

Front

What does it mean for a function to be discrete?

Back

A discrete function consists of distinct, separate values. Its graph is made up of individual points rather than a continuous line.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Front

What does it mean for a function to be continuous?

Back

A continuous function has no breaks, jumps, or holes in its graph. It can be drawn without lifting the pencil from the paper.

Front

What is the difference between discrete and continuous functions?

Back

Discrete functions consist of separate points, while continuous functions form a smooth line or curve without breaks.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Front

What is an example of a discrete function?

Back

An example of a discrete function is the number of students in a classroom, as you cannot have a fraction of a student.

Front

What is an example of a continuous function?

Back

An example of a continuous function is the height of a plant over time, as it can take on any value within a range.

Front

What does it mean for a function to be neither discrete nor continuous?

Back

A function that is neither discrete nor continuous has sections that are continuous but does not form a single line or curve.

Tags

CCSS.HSF-IF.C.7B

Front

How can you determine if a function is linear or nonlinear?

Back

You can determine if a function is linear or nonlinear by examining its graph. If it forms a straight line, it is linear; if it curves, it is nonlinear.

Tags

CCSS.8.F.A.3

Front

What is the significance of the slope in a linear function?

Back

The slope (m) in a linear function indicates the steepness of the line and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.

Tags

CCSS.8.EE.B.5