For each of the following, determine whether the equation defines $y$ as a function of $x$.
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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 $\boxed{{\displaystyle \text{function}}}$.