The problem asks to determine whether the given correspondence between the domain and range is a function.

In mathematics, a relation is a function if every element in the domain corresponds to exactly one element in the range. This means that for each input from the domain, there must be only one output in the range.

Let's analyze the provided diagram:

• $x$ maps to $Y$
• $z$ maps to both $Z$ and $X$
• $e$ maps to $W$
• $g$ maps to $U$

Conclusion:

This correspondence is not a function because the element $z$ in the domain maps to two elements in the range ($Z$ and $X$). For a correspondence to be a function, each domain element must map to only one range element.

Would you like further details or have any other questions?

Here are some related questions for deeper understanding:

1. What defines a one-to-one function, and how does it differ from a general function?
2. Can a function have repeated elements in the range? Why or why not?
3. How would the diagram change to make this relation a function?
4. What is the difference between domain and codomain in functions?
5. How can you determine the inverse of a function if one exists?

Tip: When determining if a relation is a function, always check that each element in the domain maps to one and only one element in the range.