Answer
$$
f(x)=\frac{x+2}{x^{2}-4}
$$
is continuous for all real numbers x except $x = 2$ , $ x = -2.$
Work Step by Step
$$
f(x)=\frac{x+2}{x^{2}-4}
$$
The function being graphed is a rational function, and hence is continuous at every number where the denominator is nonzero.
Solving the equation
$$
x^{2}-4=0
$$
yields discontinuities at $x = 2$ and at $ x = -2$ (Figure 1)
$$
f(x)=\frac{x+2}{x^{2}-4}
$$
is continuous for all real numbers x except $x = 2$ , $ x = -2$
