Linear vs Nonlinear functions

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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.

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CCSS.8.F.A.1

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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.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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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.

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CCSS.8.F.A.3

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

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What does it mean for a function to be linear?

Back

A linear function has a constant slope 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 does it mean for a function to be nonlinear?

Back

A nonlinear function does not have a constant rate of change and cannot be expressed in the form y = mx + b.

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CCSS.8.F.A.3

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What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-coordinate to the change in the x-coordinate (rise over run).

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CCSS.8.EE.B.5

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What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2.

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CCSS.8.F.A.3

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What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1