#### Answer

$$
f(x)=\frac{x+2}{x^{2}+4}
$$
Therefore, the function $f(x)=\frac{x+2}{x^{2}+4} $ is continuous for all real values of $x$.

#### 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
$$
x^{2}+4=0
$$
this equation has no real solution
Therefore, the function $f(x)=\frac{x+2}{x^{2}+4} $ is continuous for all real values of $x$.