To determine whether the given function is one-to-one, we need to check if each input (or domain value) maps to a unique output (or range value).

The given set of points is:

$\{(9, 9), (10, 10), (11, 43), (12, 65)\}$

Steps to check if the function is one-to-one:

1. A function is one-to-one if no two different domain values map to the same range value.

2. In other words, if there are any duplicate y-values, the function will not be one-to-one.

Checking the y-values:

• The first point is $(9, 9)$, so the range value is 9.
• The second point is $(10, 10)$, so the range value is 10.
• The third point is $(11, 43)$, so the range value is 43.
• The fourth point is $(12, 65)$, so the range value is 65.

There are no repeated range values (9, 10, 43, and 65 are all unique).

Conclusion:

Since all the y-values are distinct, this function is one-to-one.

Would you like more details on this topic? Or do you have any questions about this process?

Here are some related questions you might find interesting:

1. What is the formal definition of a one-to-one function?
2. How can you check if a function is one-to-one using its graph?
3. How can we determine if a function is not one-to-one using a set of ordered pairs?
4. How do one-to-one functions relate to invertibility?
5. Can a function be both one-to-one and onto?

Tip: If a function's graph passes the Horizontal Line Test, it's a quick way to check if the function is one-to-one.