Exponential Functions

Transformations of exponential functions

Properties of exponents

Exponential Growth versus Exponential Decay

Domain and Range

Basic shape of the graph of a parent exponential function

Example of application

Asymptotes

The asymptote is the line that is closet to the x-axis

On a function, it is the number that adds or subtracts to the rest of it

Exponential growth is greater constant increase of with time

Exponential decay is constant decrease with time

Domain

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It is what creates the line curve on the graph

In exponential decay, the total value decreases but the proportion that leaves remains constant over time

It also creates the curve on the graph

On a function, if A is positive and B is greater than 1, then it is exponential growth

On a function, if A is positive and B is less than 1 but greater than 0, then it is exponential decay.

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The domain of exponential functions is all real numbers.

Range

The range is all real numbers greater than zero.