Linear vs Nonlinear Functions

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What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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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 graph to a straight line. Its graph can be a curve, a circle, or any other shape that is not a straight line.

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CCSS.8.F.A.3

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What is the slope in a linear function?

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The slope (m) in a linear function represents the rate of change of the function. It indicates how much y changes for a unit change in x.

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CCSS.8.EE.B.5

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What does the y-intercept represent in a linear function?

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The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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Give 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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Give an example of a nonlinear function.

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

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CCSS.8.F.A.3

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How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How can you identify a nonlinear function from its graph?

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A nonlinear function can be identified by its curved graph, which does not have a constant slope.

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CCSS.8.F.A.3

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What is the general form of a linear equation?

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

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What is the difference between a function and a relation?

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

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CCSS.8.F.A.1