Linear vs Nonlinear Functions

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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.

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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 can have curves or bends.

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CCSS.8.F.A.3

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified by a straight line on the graph.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does it mean for a function to have a constant rate of change?

Back

A constant rate of change means that for every unit increase in x, the value of y increases by a fixed amount.

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CCSS.HSF-LE.A.1B

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

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CCSS.8.EE.B.5

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What is a y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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Can a function be both linear and nonlinear?

Back

No, a function cannot be both linear and nonlinear. It must fit one definition or the other.

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CCSS.8.F.A.3

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which creates a parabola when graphed.

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CCSS.8.F.A.3

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

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CCSS.8.F.A.1