Exponential vs Linear 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.HSF.LE.A.2

CCSS.8.F.B.4

Front

What is an exponential function?

Back

An exponential function is a function in which an independent variable appears 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 can 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. The differences in y-values divided by the differences in x-values will be the same.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

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

Back

An exponential function will show a constant multiplicative rate of change. The ratio of consecutive y-values will be constant.

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CCSS.HSF-LE.A.1A

Front

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. 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?

Back

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

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CCSS.8.F.A.3

CCSS.8.EE.B.6

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 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

Front

How does the graph of a linear function look?

Back

The graph of a linear function is a straight line that can slope upwards or downwards depending on the sign of the slope.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

How does the graph of an exponential function look?

Back

The graph of an exponential function shows a rapid increase or decrease, forming a curve that gets steeper as x increases.

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CCSS.HSF-IF.C.7E