Exponential vs Linear 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 number), and x is the exponent. The graph of an exponential function is a curve that increases or decreases rapidly.

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

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A linear function will have a constant rate of change between the x-values and y-values. This means that 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 do you identify an exponential function from a table of values?

Back

An exponential function will have a constant ratio of change between the y-values as x increases. This means that the ratio of y-values for consecutive x-values will be the same.

Tags

CCSS.HSF-LE.A.1A

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What is the slope in a linear function?

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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.

Tags

CCSS.8.EE.B.5

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What does the y-intercept represent in a linear function?

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

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the general form of an exponential growth function?

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The general form of an exponential growth function is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

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What is the general form of an exponential decay function?

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The general form of an exponential decay function is y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

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What is the difference between linear and exponential growth?

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

Front

What does it mean if a function is neither linear nor exponential?

Back

If a function is neither linear nor exponential, it does not fit the characteristics of either type, meaning it may have a more complex relationship between x and y.