## Precalculus (6th Edition) Blitzer

The function $f$ is continuous at $x=2$.
Recall that if $f$ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$. $\lim_\limits{x\to 2} f(x)=\lim_\limits{x\to 2} (2-x)=0$ at $x=2$ and $\lim_\limits{x\to 2} f(x)=\lim_\limits{x\to 2} (x^2-2x)=0$ at $x=2$ So, $\lim_\limits{x\to 2} (2-x)= \lim_\limits{x\to 2} (x^2-2x)$ Therefore, the function $f$ is continuous at $x=2$