Use the following information to answer the next question A student is trying to determine the domain of $h(x)=f(x)-g(x)$ using the functions $f(x)=-\sqrt{x-3}$ and $g(x)=x^{2}+3 x-8$. Their possible answers for the domain are listed below. \begin{tabular}{|c|c|c|c|c|} \hline Reference & Form & & Reference & $a$ \\ \hline 1 & {$[a, \infty)$} & & 4 & -8 \\ \hline 2 & $(-\infty, a]$ & & 5 & -3 \\ \hline & & & 6 & 3 \\ \hline & & & 7 & 8 \\ \hline \end{tabular} Numeric Response \[ (-\sqrt{x-3})-\left(x^{2}+3 x-0\right) \] 2. The correct form the domain can be written in is represented by reference number , and the correct value of $a$ is represented by reference number (Record your answer in the numerical-response section on the answer sheet.)

Step 1 ：The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. The domain of a function is the set of all possible x-values which will make the function "work", and will output real y-values.

Step 2 ：For the function \(h(x)=f(x)-g(x)\), the domain is the set of all x-values that are in the domain of both \(f(x)\) and \(g(x)\).

Step 3 ：The function \(f(x)=-\sqrt{x-3}\) is defined for all \(x \geq 3\), because the expression under the square root must be non-negative.

Step 4 ：The function \(g(x)=x^{2}+3 x-8\) is a polynomial, and is defined for all real numbers.

Step 5 ：Therefore, the domain of \(h(x)\) is the intersection of the domains of \(f(x)\) and \(g(x)\), which is \([3, \infty)\).

Step 6 ：The correct form the domain can be written in is represented by reference number 1, and the correct value of \(a\) is represented by reference number 6.

Step 7 ：Final Answer: \(\boxed{1, 6}\)