Let's go through the exercises one by one, addressing the tasks and answering any missing questions on the sheet.

Part 1: Identifying Functions

Question 3:

Points: $(6, -7), (8, -10), (5, -7), (8, -7)$

• Is it a function? The answer is no because $x = 8$ corresponds to two different $y$ values: $-10$ and $-7$. A function must assign exactly one $y$ value to each $x$ value.

Question 4:

Points: $(4, -1), (3, -1), (1, -1), (0, -1), (-9, -1)$

• Is it a function? The answer is yes, as every $x$ value has a unique corresponding $y$ value.

Part 2: Relations Represented as Tables

1. Table: \hline x & y \\ \hline 1 & 3 \\ -2 & -4 \\ 4 & 6 \\ \hline \end{array}$$ - **Is it a function?** Yes. Every $$x$$ value has a unique $$y$$ value. - **Domain:** $$\{1, -2, 4\}$$ - **Range:** $$\{3, -4, 6\}$$
2. Table: \hline x & y \\ \hline 0 & 3 \\ -3 & 3 \\ 10 & 9 \\ \hline \end{array}$$ - **Is it a function?** Yes. Each $$x$$ value has a unique $$y$$ value. - **Domain:** $$\{0, -3, 10\}$$ - **Range:** $$\{3, 9\}$$

You Try:

1. Table: \hline x & y \\ \hline -6 & -3 \\ -6 & -6 \\ -6 & 1 \\ -6 & 9 \\ \hline \end{array}$$ - **Is it a function?** No, because the same $$x$$ value $$-6$$ corresponds to multiple $$y$$ values. - **Domain:** $$\{-6\}$$ (Only one unique $$x$$) - **Range:** $$\{-3, -6, 1, 9\}$$
2. Table: \hline x & y \\ \hline -1 & 2 \\ 3 & 0 \\ -6 & -8 \\ 1 & 3 \\ \hline \end{array}$$ - **Is it a function?** Yes, each $$x$$ value is paired with one unique $$y$$ value. - **Domain:** $$\{-1, 3, -6, 1\}$$ - **Range:** $$\{2, 0, -8, 3\}$$

Would you like more details on any part of this solution? Here are five related questions to consider:

1. How do you formally define a function in mathematics?
2. Can a function have repeating $y$ values? Why or why not?
3. What is the difference between the domain and range in a relation?
4. How do you check whether a set of ordered pairs represents a function?
5. Why is it important that each $x$ value in a function corresponds to only one $y$ value?

Tip: When analyzing a relation, always look at the $x$ values first to ensure that each one has only a single output in the corresponding $y$ values!