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Exponential Functions - Coggle Diagram
Exponential Functions
Exponential Growth versus Exponential Decay
Exponential growth is greater constant increase of with time
It is what creates the line curve on the graph
On a function, if A is positive and B is greater than 1, then it is exponential growth
Exponential decay is constant decrease with time
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 less than 1 but greater than 0, then it is exponential decay.
Domain and Range
Domain
The domain of exponential functions is all real numbers.
Range
The range is all real numbers greater than zero.
Basic shape of the graph of a parent exponential function
Transformations of exponential functions
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
Properties of exponents