The graph provided appears to represent a portion of a function, and you are asking to determine if it is one-to-one using the horizontal line test.

Horizontal Line Test

A function is one-to-one if and only if any horizontal line intersects the graph at most once. This means that each value of $y$ should correspond to only one value of $x$, indicating that the function has no repeating $y$-values for different $x$-values.

Analysis of the Graph

The graph shows a curve resembling a portion of a rational or exponential function that decreases rapidly in the first quadrant and extends into the second quadrant (as $x \to 0$ from the left and $y \to +\infty$).

If we draw horizontal lines across the graph, each horizontal line intersects the curve only once for each $y$-value. This confirms that no $y$-value corresponds to more than one $x$-value.

Conclusion

Since no horizontal line intersects the graph more than once, the function passes the horizontal-line test, and it is a one-to-one function.

Would you like further details or have any specific questions about this?
Here are some related questions to explore this concept further:

1. What kind of functions generally pass the horizontal line test?
2. How does the horizontal line test relate to the function's inverse?
3. Can a polynomial function be one-to-one?
4. What are examples of functions that fail the horizontal-line test?
5. How does the graph of a one-to-one function differ from a non-one-to-one function?

Tip: Inverse functions exist only for one-to-one functions, so passing the horizontal-line test ensures that the function has an inverse!