In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2^(x+1)

Exponential functions are mathematical expressions in the form f(x) = a^x, where 'a' is a positive constant. They are characterized by their rapid growth or decay, depending on the base. The function f(x) = 2^x, for example, increases as x increases, and approaches zero as x approaches negative infinity, illustrating the behavior of exponential growth.

Transformations of functions involve shifting, stretching, compressing, or reflecting the graph of a function. For instance, the function g(x) = 2^(x+1) represents a horizontal shift of the graph of f(x) = 2^x to the left by one unit. Understanding these transformations is crucial for accurately graphing new functions based on known ones.

Asymptotes are lines that a graph approaches but never touches. For exponential functions like f(x) = 2^x, the horizontal asymptote is typically the x-axis (y = 0). Identifying asymptotes helps in determining the behavior of the function as x approaches certain values, which is essential for understanding the domain and range of the function.