To determine if the given relation is a function, we need to verify if each input $x$ corresponds to exactly one output $y$. This means that for each unique $x$-coordinate, there should be exactly one $y$-coordinate.

Let's examine the points provided:

1. $(-5, 1)$
2. $(-3, 0)$
3. $(0, -3)$
4. $(2, 3)$
5. $(5, -1)$
6. $(5, 1)$

Notice that the $x$-coordinate 5 has two different $y$-coordinates: $-1$ and $1$. This indicates that for the input $x = 5$, there are two different outputs, $-1$ and $1$.

Therefore, the relation is not a function because there is at least one input that corresponds to more than one output.

The correct explanation is: No, because for each input there is not exactly one output.

Do you want details or have any questions?

Here are 5 more questions you might find interesting:

1. How do you determine the domain and range of a function?
2. What is the vertical line test, and how does it help identify functions?
3. Can a function have two different inputs with the same output?
4. What are the characteristics of a one-to-one function?
5. How do you find the inverse of a function, and when does it exist?

Tip: Always remember that in a function, each input must map to exactly one output. This is the key property that distinguishes functions from general relations.