The equation y = k^x describes which type of function?

The equation y = k^x is an example of an exponential function because the variable x appears as an exponent. In this equation, k is a constant base that is raised to the power of x, which means that as x changes, the value of y changes exponentially.

Exponential functions are characterized by their rapid growth (or decay) as x increases or decreases if k is greater than one (growth) or a fraction between 0 and 1 (decay). This distinguishes them from other types of functions.

For instance, polynomial functions are defined by terms that include x raised to whole number powers, and they do not exhibit the same rapid growth patterns as exponential functions. Logarithmic functions, on the other hand, are the inverses of exponential functions and represent the logarithm of a variable. Rational functions consist of ratios of polynomials and do not take the form y = k^x.

Therefore, y = k^x is clearly classified as an exponential function due to its unique properties related to the exponentiation of a constant base.