Exponential Functions from Tables

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What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

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What does the base in an exponential function represent?

Back

The base in an exponential function determines the growth or decay rate of the function. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Tags

CCSS.HSF-IF.C.8B

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

Back

An exponential function can be identified from a table of values if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by the same amount.

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CCSS.HSF-LE.A.1A

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What is the common ratio in an exponential sequence?

Back

The common ratio in an exponential sequence is the factor by which each term is multiplied to get the next term. It is constant throughout the sequence.

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CCSS.HSF.BF.A.2

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Given the function f(x) = 2(6)^x, what is the common ratio?

Back

The common ratio is 6.

Tags

CCSS.HSF-IF.C.8B

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What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, represented by a straight line, while exponential functions have a variable rate of change that increases or decreases rapidly, represented by a curve.

Front

How can you determine if a function is exponential from its graph?

Back

A function is exponential if its graph shows a rapid increase or decrease, forming a curve that gets steeper or shallower, rather than a straight line.

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What is the general form of an exponential function?

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The general form of an exponential function is f(x) = a(b)^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Front

If f(x) = 27(1/3)^x, what type of function is this?

Back

This is an exponential decay function because the base (1/3) is less than 1.

Tags

CCSS.HSF-IF.C.8B

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What does it mean for a function to be exponential?

Back

A function is considered exponential if it can be expressed in the form f(x) = a(b)^x, where the variable x is in the exponent.