Graph y= 2^x and x = 2^y in the same rectangular coordinate system.

Exponential functions are mathematical expressions in the form y = a^x, where 'a' is a positive constant and 'x' is the variable. These functions exhibit rapid growth or decay, depending on the base 'a'. In the context of the question, y = 2^x represents an exponential growth function, where as 'x' increases, 'y' increases exponentially.

Inverse functions are functions that reverse the effect of the original function. For a function f(x), its inverse f^(-1)(x) satisfies the condition f(f^(-1)(x)) = x. In this case, the equation x = 2^y can be rewritten as y = log2(x), which is the inverse of the exponential function y = 2^x. Understanding this relationship is crucial for graphing both functions.

Graphing in a rectangular coordinate system involves plotting points on a two-dimensional plane defined by an x-axis (horizontal) and a y-axis (vertical). Each point is represented by an ordered pair (x, y). To graph y = 2^x and x = 2^y, one must plot the exponential growth of y = 2^x and its inverse, y = log2(x), to visualize their intersection and behavior in the coordinate system.