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The function f(x) = ax is the exponential function with base a. Given this definition, provide an example of an exponential function, discuss the behavior and give the domain of the provided exponential function.

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Answer:

The function f(x)=3x is an exponential function; the variable is the exponent. If f(x) = ax, then we call a the base of the exponential function. The base must always be positive. In fact, for any real number x, 1x = 1, so f(x)=1x is the same function as the constant function f(x) = 1.

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