linear vs exponential functions

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What is a linear function?

Back

A linear function is a function that graphs to a straight line. 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

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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 = 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 graph?

Back

A linear function will show a straight line when graphed, indicating a constant rate of change.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How can you identify an exponential function from a graph?

Back

An exponential function will show a curve that increases or decreases rapidly, indicating a variable rate of change.

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CCSS.HSF-IF.C.7E

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What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

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CCSS.8.EE.B.5

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What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.

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What is the difference between linear and exponential growth?

Back

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

Front

If a function doubles every week, what type of function is it?

Back

It is an exponential function.

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CCSS.HSF-LE.A.1A

Front

If a function increases by 2 each week, what type of function is it?

Back

It is a linear function.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a real-world example of a linear function?

Back

A real-world example of a linear function is the relationship between distance and time at a constant speed.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2