Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - 14.3 One-sided Limits; Continuous Functions - 14.3 Assess Your Understanding - Page 891: 58

not continuous

$f(x)$ will be continuous at $x=2$ if $f(2)=\lim_{x\to 2}f(x)$. We know that $f(2)=2$. $$\lim_{x\to 2^+}f(x)\\=\lim_{x\to 2^+}\frac{x-4}{x-1}\\=\lim_{x\to 2^+}\frac{2-4}{2-1}\\=\frac{-2}{1}=-2$$ $-2\ne2$, hence it is not continuous at $2$.