Linear vs Exponential

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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 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 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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How does a linear function grow?

Back

A linear function grows at a constant rate. For every unit increase in x, y increases by a fixed amount.

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CCSS.HSF-LE.A.1B

Front

How does an exponential function grow?

Back

An exponential function grows at an increasing rate. As x increases, y increases by a larger and larger amount.

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CCSS.HSF-IF.C.8B

Front

What is the general shape of a linear graph?

Back

The graph of a linear function is a straight line.

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CCSS.HSF-IF.C.7A

Front

What is the general shape of an exponential graph?

Back

The graph of an exponential function is a curve that rises rapidly.

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CCSS.HSF-IF.C.7E

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What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of y with respect to x.

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CCSS.8.EE.B.5

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What does the base represent in an exponential function?

Back

The base (b) in an exponential function determines the growth rate. If b > 1, the function grows; if 0 < b < 1, the function decays.

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CCSS.HSF-IF.C.8B

Front

Give 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

Front

Give an example of an exponential function.

Back

An example of an exponential function is y = 3(2^x).