For each of the following, determine whether the equation defines $y$ as a function of $x$. \begin{tabular}{|c|c|c|} \hline$y=9 \mid x-3$ & Function & Not a function \\ \hline $36=|y|+x^{2}$ & Function & Not a function \\ \hline $36+y^{2}=x^{2}$ & Function & Not a function \\ \hline $3 x=y^{3}$ & Function & (1) Not a function \\ \hline & & 5 \\ \hline \end{tabular}

Step 1 ：The question is asking whether the given equations define y as a function of x. A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. In other words, for each x, there should be exactly one y.

Step 2 ：Let's start with the first equation: \(y=9 |x-3|\)

Step 3 ：This equation is a function because for each value of x, there is exactly one value of y. The absolute value function is a function because it passes the vertical line test. The vertical line test is a visual way to determine if a curve is a graph of a function or not. If we can draw any vertical line that intersects a graph more than once, then the graph does not define y as a function of x.

Step 4 ：The plot of the function \(y=9 |x-3|\) shows that it passes the vertical line test. Therefore, it is a function.

Step 5 ：Final Answer: \(y=9 |x-3|\) is a \(\boxed{\text{function}}\).