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 890: 55

continuous

$f(x)$ will be continuous at $x=0$ if $f(0)=\lim_{x\to 0}f(x)$. We know that $f(0)=-1$. $$\lim_{x\to 0}f(x)\\=\lim_{x\to 0}\frac{x^2+3x}{x^2-3x}\\=\lim_{x\to 0}\frac{x(x+3)}{x(x-3)}\\=\lim_{x\to 0}\frac{(x+3)}{(x-3)}\\=\frac{(0+3)}{(0-3)}=-1$$ $-1=-1$, hence it is continuous at $0$.