The function f(x) = e^x represents an exponential function where the base e is approximately equal to 2.71828. This function is unique because it is its own derivative, meaning that the rate of change of f(x) at any point is equal to its value at that point. This property makes it important in calculus and various applications in science and engineering. The graph of f(x) = e^x is a smooth curve that rises steeply as x increases and approaches zero as x decreases. It never touches the x-axis, indicating that f(x) is always positive. This behavior is significant in fields such as finance, where it models continuous growth, and population dynamics, where it describes exponential growth patterns.