Modulus Function

The modulus function, written as $f(x) = |x|$, is a simple but powerful idea: it gives the distance of a number from zero on the number line, so it always returns a non-negative value. What makes it special in calculus is its sharp corner at $x = 0$ — the graph changes direction abruptly, meaning the function is not differentiable at that point. This single kink makes $|x|$ the perfect example for understanding where a function can be continuous yet not smooth, and it forces yo …