Mathematics

The key is recognizing that the absolute value creates a piecewise function with different behavior on either side of $x = 2$. Since $|x - 2|$ equals $(x - 2)$ when $x \geq 2$ and $(2 - x)$ when $x < 2$, the square root function will have a sharp corner (cusp) at $x = 2$ rather than a smooth curve. Understanding this shape—and whether $f$ is continuous, differentiable, or has other properties—will help you evaluate which statement holds.

The key is recognizing that the absolute value creates a piecewise function with different behavior on either side of $x = 2$. Since $|x - 2|$ equals $(x - 2)$ when $x \geq 2$ and $(2 - x)$ when $x < 2$, the square root function will have a sharp corner (cusp) at $x = 2$ rather than a smooth curve. Understanding this shape—and whether $f$ is continuous, differentiable, or has other properties—will help you evaluate which statement holds.