Linear vs Exponential Functions

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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 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

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What is an exponential function?

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An exponential function is a function in which an independent variable appears in the exponent. It has the form y = a(b^x), where a is a constant, b is the base, and x is the exponent.

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

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A linear function will have a constant rate of change, meaning the difference between consecutive y-values divided by the difference between consecutive x-values is the same.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

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How can you identify an exponential function from a table of values?

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An exponential function will have a constant ratio of consecutive y-values when divided by the previous y-value, indicating that the y-values are increasing or decreasing by a constant factor.

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CCSS.HSF-LE.A.1A

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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 y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.F.A.3

CCSS.8.EE.B.6

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What is the general form of an exponential equation?

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The general form of an exponential equation is y = a(b^x), where a is a constant, b is the base, and x is the exponent.

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CCSS.HSF.LE.A.2

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What does the slope of a linear function represent?

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The slope of a linear function represents the rate of change of y with respect to x. 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 base of an exponential function represent?

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The base of an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

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CCSS.HSF-IF.C.8B

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If a function has a constant increase of 3 for every increase of 1 in x, what type of function is it?

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It is a linear function.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

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If a function doubles in value for every increase of 1 in x, what type of function is it?

Back

It is an exponential function.

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CCSS.HSF-LE.A.1A