We are given a function $g: S \to S$, where the set $S = \{-10, -5, 0, 5, 10\}$, and the table provides some values of the function $g$ corresponding to different inputs $y$.

The table looks like this:

We are asked to determine the following missing values:

1. $g(0)$ — Referring to the table, we see $g(0) = 10$.

2. $g(5)$ — Referring to the table, we see $g(5) = -5$.

3. $g(\text{?}) = 0$ — We need to determine which input $y$ gives $g(y) = 0$. According to the table, $g(-5) = 0$.

Final Answers:

1. $g(0) = 10$
2. $g(5) = -5$
3. $g(\text{?}) = 0$ — The answer is $y = -5$.

Would you like more details, or do you have any questions?

Here are 5 related questions for further practice:

1. What is the inverse of the function $g$ based on the given table?
2. How many different outputs can a function from a set to itself have?
3. What is the composition of $g$ with itself, i.e., $g(g(y))$ for all $y \in S$?
4. If we defined a new function $f: S \to S$ as $f(y) = -g(y)$, what would the table of $f$ look like?
5. How does knowing the function’s behavior affect its invertibility?

Tip: When given a function in a table format, always match the input-output pairs carefully to spot patterns or missing values.