To determine which tables represent $y$ as a function of $x$ and are one-to-one, let's analyze each table in the image.

Criteria:

1. Function: Each $x$ value must correspond to exactly one $y$ value.
2. One-to-One: Each $y$ value must correspond to exactly one $x$ value (no repeated $y$ values).

Analysis:

1. First Table:

   • $x$: [5, 7, 11]
   • $y$: [4, 9, 9]
   • The $y$ values repeat (9 is listed twice), so it is not one-to-one.
   • It is a function since each $x$ has only one $y$, but it fails the one-to-one condition.

2. Second Table:

   • $x$: [5, 7, 11]
   • $y$: [4, 9, 14]
   • The $y$ values are all distinct.
   • Each $x$ maps to a unique $y$, and there are no repeated $y$ values, so it is both a function and one-to-one.

3. Third Table:

   • $x$: [5, 7, 7]
   • $y$: [4, 9, 14]
   • The $x$ value 7 is repeated, mapping to two different $y$ values (9 and 14), so it is not a function.

Conclusion:

• First Table: Function but not one-to-one.
• Second Table: Function and one-to-one.
• Third Table: Not a function.

Answer: Only the second table represents $y$ as a function of $x$ and is one-to-one.

Would you like more details or have any questions?

Related Questions:

1. What is the definition of a one-to-one function?
2. How can you determine if a set of points is a function using the vertical line test?
3. What is the horizontal line test for one-to-one functions?
4. Can a function be one-to-one if its $x$ values repeat?
5. How would the answer change if the $y$ values of the first table were all unique?

Tip: For a quick check, use the vertical line test for functions and the horizontal line test for one-to-one functions!