Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 99: 102

See graph and explanations.

See graph; when $x\to-2^+, y\to\infty$ or $\lim_{x\to -2^+}\frac{x^2-1}{2x+4}=\infty$; while when $x\to-2^-, y\to-\infty$ or $\lim_{x\to -2^-}\frac{x^2-1}{2x+4}=-\infty$; the asymptote of the function is $x=-2$