To determine if the graph represents a one-to-one function, we need to verify the Horizontal Line Test: if any horizontal line crosses the graph at more than one point, the function is not one-to-one.

Analysis:

From the image:

• The graph crosses some horizontal lines (e.g., $y = 1$, $y = 2$) more than once.
• This implies the function fails the Horizontal Line Test.

Conclusion:

The function shown in the graph is not one-to-one.

Would you like further clarification or a detailed explanation of the Horizontal Line Test?

Related Questions:

1. What is the Vertical Line Test, and how does it differ from the Horizontal Line Test?
2. Can a non-one-to-one function be modified to make it one-to-one?
3. What are examples of functions that always pass the Horizontal Line Test?
4. How can the concept of inverse functions relate to one-to-one functions?
5. What are some practical applications of one-to-one functions in real-world scenarios?

Tip:

For any function $f(x)$, a one-to-one function must satisfy $f(a) \neq f(b)$ for all $a \neq b$.