Answer
\[\text{Continuous for all real numbers except }t=\pm 2\]
Work Step by Step
\[\begin{align}
& f\left( t \right)=\frac{t+2}{{{t}^{2}}-4} \\
& \text{See the theorem 2}\text{.10 }\left( \text{page 101} \right) \\
& a.\text{ A polynomial function is continuous for all }x \\
& b.\text{ A rational function }\left( \text{a function of the form }\frac{p}{q},\text{ where }p \right. \\
& \text{ and }q\text{ are }\left. \text{polynomials} \right)\text{is continuous for all }x\text{ for which }q\ne 0 \\
& \text{ For }f\left( t \right)=\frac{t+2}{{{t}^{2}}-4}\Rightarrow p\left( t \right)=t+2\text{ and }q\left( t \right)={{t}^{2}}-4 \\
& \text{ }q\left( t \right)\ne 0,\text{ then} \\
& {{t}^{2}}-4\ne 0 \\
& {{t}^{2}}\ne 4 \\
& t\ne \pm 2 \\
& \text{The function is not continuous for }t= \pm 2,\text{ then is} \\
& \text{continuous for all real numbers except }t=\pm 2 \\
\end{align}\]
