## Calculus: Early Transcendentals (2nd Edition)

When $x\neq 1$ this is a linear function in disguise: $$f(x)=\frac{x^2-x}{x-1}=\frac{x(x-1)}{x-1}=x$$ and it was legal to cancel the term $x-1$ because $x\neq1$. So this function can be rewritten as $$f(x)=\bigg\{_{x,\quad x\neq1.}^{2,\quad x=1;}.$$ This function is given on the graph below where the filled circle says that the endpoint is included while the empty circle means that the endpoints are excluded