Linear vs Exponential Functions

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What is a linear function?

Back

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

Tags

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 appears in the exponent. It can be expressed in the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

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

Back

A linear function will have a constant rate of change, meaning the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

An exponential function will have a constant ratio of consecutive y-values when the x-values increase by the same amount.

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CCSS.HSF-LE.A.1A

Front

What does the graph of a linear function look like?

Back

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

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the graph of an exponential function look like?

Back

The graph of an exponential function is a curve that increases or decreases rapidly, often resembling a J-shape or an L-shape.

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CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) in a linear function is the value of y when x is 0.