The question is asking which of the given tables shows $y$ as a function of $x$. In mathematics, for $y$ to be a function of $x$, each value of $x$ must correspond to exactly one value of $y$. In other words, no $x$-value should be paired with more than one $y$-value.

Let's analyze each table:

Table F:

• $x = -13$, $y = -2, 0, 5, 7$
• The same $x$-value of $-13$ corresponds to multiple $y$-values (−2, 0, 5, 7), so this is not a function.

Table G:

• $x = -6$, $y = 3$
• $x = -1$, $y = -1, 5$
• $x = 10$, $y = -9$
• The same $x$-value of $-1$ corresponds to two different $y$-values (−1, 5), so this is not a function.

Table H:

• $x = 1$, $y = 4$
• $x = 3$, $y = 4$
• $x = 7$, $y = 4$
• $x = 12$, $y = 4$
• Each $x$-value corresponds to exactly one $y$-value (in this case, all are $4$), so this is a function.

Table J:

• $x = -9$, $y = -7$
• $x = -2$, $y = -5$
• $x = 0$, $y = 0, 6$
• The $x$-value of $0$ corresponds to two different $y$-values (0, 6), so this is not a function.

Conclusion:

The correct table that shows $y$ as a function of $x$ is Table H.

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

Here are 5 related questions:

1. What is the definition of a function in mathematics?
2. How can we tell if a set of points represents a function?
3. What is the difference between a function and a relation?
4. Can a function have two identical $y$-values for different $x$-values?
5. What is the vertical line test, and how does it relate to functions?

Tip: Remember, in functions, each input (value of $x$) must map to exactly one output (value of $y$).