https://file.aiquickdraw.com/mathbot/file/1730208273887tavhcsj7.jpg

The function represented in the graph is **not one-to-one**. 

To determine whether a function is one-to-one, we can use the **Horizontal Line Test**: if any horizontal line drawn across the graph intersects it more than once, the function is not one-to-one. 

In this case, several horizontal lines would intersect the curve in multiple places (especially near the peaks and troughs), meaning the function fails the Horizontal Line Test and is therefore not one-to-one.

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What is the Vertical Line Test, and how does it determine if a curve is a function?
2. How do you define a one-to-one function mathematically?
3. What does it mean for a function to be invertible, and how does it relate to being one-to-one?
4. Can a polynomial of degree 3 or higher be one-to-one?
5. How does the shape of a graph indicate if it’s increasing or decreasing?

**Tip:** To test if a function is one-to-one, consider both its algebraic form and the graphical Horizontal Line Test.

Understand how to determine if a function is one-to-one using the Horizontal Line Test. Analyze the graph to see if any horizontal line intersects the curve more than once, which would indicate that the function is not one-to-one. Suitable for high school students studying functions and graph analysis.

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