Main Concept

A constant function is a function whose range consists of a single element. That is, the output value of the function at any input value in its domain is the same, independent of the input. The mathematical formula for a constant function is just $f\left(x\right)\=a$, where $a$ is a number (which does not depend on $x$). The graph of a constant function is a horizontal line, that is, a line with slope 0.

Note: it is not necessary for the (single) value of the function, the "$a$" in the discussion above, to be literally a number, such as 3 or 0 or $\mathrm{\π}$. All that matters is that the output, whatever it is, it does not depend on the input variable, $x$. For example, the function $f\left(x\right)\=w^2$ is a constant function with respect to its input variable, x.

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