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 has 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 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 the graph of a linear function look?

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

How does the graph of an exponential function look?

Back

The graph of an exponential function is a curve that increases or decreases rapidly, showing exponential growth or decay.

Tags

CCSS.HSF-IF.C.7E

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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.

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What is the formula for calculating the value of an exponential function?

Back

The formula is y = ab^x, where a is the initial value, b is the growth factor, and x is the time or number of periods.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean for a function to decrease by a percentage each year?

Back

It means that the value of the function is multiplied by a factor less than 1 each year, indicating exponential decay.

Tags

CCSS.HSF-IF.C.8B

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.

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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 (b) is the value of y when x is 0, indicating where the line crosses the y-axis.

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Can a linear function ever be exponential?

Back

No, a linear function cannot be exponential. They are distinct types of functions with different properties.