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The typical rational function has the form p(x)/q(x) where p and q are polynomials. p(x) is called the numerator and q(x) is called the denominator. Example: In the rational function. which simplifies to simplifies to (x+2)/(x-3), but the x = 2 is NOT in the domain of g(x) whereas it IS in the domain of (x+2)/(x-3).
Exponential functions are functions of the form f(x) = bx for a fixed base b which could be any positive real number. Exponential functions are characterized by the fact that their rate of growth is proportional to their value. For example, suppose we start with a population of cells such that its growth rate at any time is proportional to its size.