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Determine whether the function graphed is one-to-one.
Is the function graphed one-to-one?
Yes, at least one horizontal line intersects the graph at more than one point.
No, every horizontal line intersects the graph at exactly one point.
No, at least one horizontal line intersects the graph at more than one point.
Yes, every horizontal line intersects the graph at exactly one point.

The graph shown is a parabola, which opens downward. To determine whether the function is one-to-one, we use the **horizontal line test**. 

- A function is **one-to-one** if and only if no horizontal line intersects the graph at more than one point.
- In this case, the parabola fails the horizontal line test because some horizontal lines (for example, those near the vertex of the parabola) will intersect the graph at two points.

Therefore, the correct answer is:

**No, at least one horizontal line intersects the graph at more than one point.**

Would you like further explanation or details? Here are five related questions you might consider:

1. What is the horizontal line test, and how does it help identify one-to-one functions?
2. How can we algebraically determine if a quadratic function is one-to-one?
3. What are the key characteristics of one-to-one functions?
4. What transformations can make a non-one-to-one function one-to-one?
5. Can a parabola ever represent a one-to-one function?

**Tip:** A quick way to check if a function is one-to-one visually is by drawing horizontal lines through the graph; if any line crosses more than once, the function is not one-to-one.

Determine whether the function graphed is one-to-one. Is the function graphed one-to-one?

Understand how to determine if a function is one-to-one by applying the Horizontal Line Test. The function graphed in this problem is a parabola, which fails the test, indicating that the function is not one-to-one. This concept is important in understanding algebra and functions.

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