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Definition of Linear Function. A function that can be graphically represented in the Cartesian coordinate plane by a straight line is called a Linear Function.
The exponential function is one of the most important functions in mathematics (though it would have to admit that the linear function ranks even higher in importance). To form an exponential function, we let the independent variable be the exponent. A simple example is the function $$f(x)=2^x.$$. As illustrated in the above graph of $f$, the exponential function increases rapidly. Exponential functions are solutions to the simplest types of dynamical systems.