Not piecewise function constant in an interval

Question

Is it possible to have a not piecewise function that can be written with a relation (any function that can be written as $y=f(x)$ for all $x$ that turns out to be constant in an interval of $x$? Say, for example, a function $y=f(x)$ where $y$ is constant for $0<x<1$.

Answer 1

How about $f(x) = \left(\dfrac{4^x\cdot \Gamma(x+1)\cdot \Gamma\left(x + \dfrac{1}{2} \right)}{\Gamma(2x+1)}\right)^2$?

This function is actually constant over all complex numbers, not just a specific interval. It always equals $\pi$.