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## Exponential Functions

Exponential functions are any function of the form
$y = a^{bx}$latex for some constants a and b.

If a and b are both positive then the graph will be an upward curve which tends to infinity as x tends to infinity and tends to 0 as x tends to negative infinity and looks something like the below. Note that all exponential graphs cut the y axis at 1.

The graph of y = 2^x (y equals 2 to the power x)

If a is positive and b is negative the graph is simply a reflection of this about the y axis to give the following graph:

The graph of y=2^-x (y equals 2 to the power of minus x)

The most import exponential graph is $y=e^x$ because the gradient of this graph is always equal to the value of $e^x$ at that point.