Answer
Domain: All real numbers
Vertical asymptotes: none
Holes: none
Work Step by Step
Given \begin{equation}
h(x)=\frac{x-3}{x^2+3 x+10}.
\end{equation} The domain of a rational function consists of all real numbers except numbers that makes the denominator equal to zero. We need to set the expression of the denominator to zero to find the numbers that make the denominator zero and exclude them from the domain of the function. However,the expression $(x^2+3 x+10)$ is never zero for all real numbers.
$$
\begin{aligned}
\textbf{Domain: All real numbers}& \\
\end{aligned}
$$ There are neither vertical asymptotes, nor holes in the graph.
