Graph f(x) = 2^x and its inverse function in the same rectangular coordinate system.

Key Concepts

Exponential Functions

Exponential functions are mathematical expressions in the form f(x) = a^x, where 'a' is a positive constant. In this case, f(x) = 2^x represents an exponential function with a base of 2. These functions exhibit rapid growth as x increases and approach zero as x decreases, making them essential for understanding their graphical behavior.

Inverse Functions

An inverse function essentially reverses the effect of the original function. For a function f(x), its inverse, denoted as f^(-1)(x), satisfies the condition f(f^(-1)(x)) = x. For the exponential function f(x) = 2^x, the inverse is the logarithmic function f^(-1)(x) = log2(x), which is crucial for graphing both functions together.

Graphing Functions

Graphing functions involves plotting points on a coordinate system to visualize their behavior. For f(x) = 2^x, the graph will show an upward curve starting from the point (0,1) and increasing rapidly. The inverse function, log2(x), will be plotted as a curve that passes through (1,0) and increases slowly, demonstrating the relationship between a function and its inverse.