6.3 Exponential Functions PRACTICE ASSIGNMENT

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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 a positive real number, and 'x' is the exponent. It represents growth or decay at a constant percentage rate.

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What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount (e.g., y = mx + b), while exponential functions increase or decrease by a constant factor (e.g., y = a * b^x).

Front

What does it mean for a function to multiply the same number each time?

Back

This describes an exponential function, where the output is multiplied by a constant factor for each unit increase in the input.

Front

What is the starting point of an exponential function?

Back

The starting point of an exponential function is the value of 'a' in the function f(x) = a * b^x, which represents the initial value when x = 0.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

If the differences between consecutive outputs are not constant but the ratios of consecutive outputs are constant, the function is exponential.

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CCSS.HSF-LE.A.1A

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What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where 'a' is the initial value and 'b' is the base that determines the growth or decay rate.

Tags

CCSS.HSF.LE.A.2

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

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CCSS.HSF-IF.C.8B

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How do you determine if a graph is exponential?

Back

A graph is exponential if it shows a rapid increase or decrease and has a characteristic curve that is not a straight line.

Tags

CCSS.HSF-IF.C.7E

Front

What is the pattern in an exponential growth table?

Back

In an exponential growth table, the values increase by multiplying by a constant factor, leading to larger gaps between consecutive values as x increases.

Tags

CCSS.HSF-LE.A.1A

Front

What is an example of an exponential function?

Back

An example is f(x) = 2^x, which doubles the output for each increase of 1 in x.