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 $x$.
