Linear vs. Exponential Functions

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What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has the form y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

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What is an exponential function?

Back

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

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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 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 of a function represent?

Back

The y-intercept of a function is the value of y when x is 0. It represents the starting point of the function on the y-axis.

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

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are constant, it is linear.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

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

Back

An exponential function will show a constant multiplicative rate of change. If the ratio of consecutive y-values is constant, it is exponential.

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CCSS.HSF-LE.A.1A

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.F.A.3

CCSS.8.EE.B.6

Front

What is the general form of an exponential equation?

Back

The general form of an exponential equation is y = ab^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 is the difference between linear and exponential growth?

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Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.

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Provide an example of a linear function.

Back

An example of a linear function is y = 2x + 3.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2