What is the standard form of a constant function?

A constant function is one that does not change with varying inputs; its output remains the same no matter the value of the input variable. In mathematical terms, this can be expressed as a function where the output is represented by a single constant value, denoted usually as 'a'. Therefore, the standard form of a constant function is simply f(x) = a, where 'a' can be any real number. This succinctly captures the essence of a constant function: it is invariant regardless of the input x.

Other forms, such as linear functions that include variables (like Kx + b or ax + b), include dependencies on x, which contradict the definition of a constant function. The function f(x) = 0, while it does represent a constant output, is a specific case of a constant function where the constant value is zero, but it does not represent all constant functions generally. Thus, the correct and most general form for a constant function is indeed f(x) = a.