Linear Functions 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

Front

What is an exponential function?

Back

An exponential function is a function of the form y = ab^x, where a is a constant, b is the base (a positive real number), and x is the exponent. It represents growth or decay.

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How can you identify a linear function from its equation?

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A linear function will have no exponents on the variable other than 1. For example, y = 2x + 3 is linear.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How can you identify an exponential function from its equation?

Back

An exponential function will have the variable in the exponent. For example, y = 3^x is exponential.

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What is the growth factor in an exponential function?

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The growth factor is the base of the exponential function, which determines how much the function grows or decays. For example, in y = 2(3^x), the growth factor is 3.

Tags

CCSS.HSF-IF.C.8B

Front

What does the slope represent in a linear function?

Back

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

Tags

CCSS.8.EE.B.5

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What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x = 0. It is the point where the line crosses the y-axis.

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What is the difference between linear growth and exponential growth?

Back

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

Front

If a function doubles every time x increases by 1, what type of function is it?

Back

It is an exponential function.

Tags

CCSS.HSF-LE.A.1A

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.