In the context of functions, what does 'b' represent in the exponential function f(x) = ab^x?

In the exponential function f(x) = ab^x, 'b' represents the base of the exponential function. This base determines how the function grows or decays as the x-values change. If 'b' is greater than 1, the function exhibits exponential growth, meaning that as x increases, f(x) increases rapidly. Conversely, if 'b' is between 0 and 1, the function demonstrates exponential decay, where f(x) decreases as x increases.

Understanding 'b' as the base is crucial because it directly influences the function's behavior and shape on a graph. The value of 'a' serves as a vertical scaling factor, while 'b' controls the rate of increase or decrease, making it central to the characteristics of the exponential function. This is why identifying 'b' as the base is key to understanding how the function operates mathematically and graphically.