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Is the function graphed one-to-one?

OA. Yes, because each x-value corresponds to only one y-value, and each y-value

corresponds to only one x-value.

Yes, every horizontal line intersects the graph at exactly one point.

No, because each x-value corresponds to every y-value, and each y-value corresponds to every x-value

No, there is a horizontal line that intersects the graph at more than one point.

From the graph shown, the function appears to be a parabola, which opens downwards.

To determine if the function is **one-to-one**, we use the **horizontal line test**. A function is one-to-one if and only if **every horizontal line intersects the graph at most once**. Looking at the graph, a horizontal line (for example, at \(y = 5\)) would intersect the parabola at two points. This indicates that the function is not one-to-one.

Thus, the correct answer is:

**No, there is a horizontal line that intersects the graph at more than one point.**

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is the vertical line test used for?
2. How can we algebraically verify if a function is one-to-one?
3. What is the significance of the inverse function in relation to one-to-one functions?
4. Can a quadratic function ever be one-to-one? Why or why not?
5. How does the horizontal line test relate to the concept of injectivity in mathematics?

**Tip:** Remember, if a function passes the horizontal line test, it has an inverse that is also a function.

Is the function graphed one-to-one?
OA. Yes, because each x-value corresponds to only one y-value, and each y-value corresponds to only one x-value.
Yes, every horizontal line intersects the graph at exactly one point.
No, because each x-value corresponds to every y-value, and each y-value corresponds to every x-value.
No, there is a horizontal line that intersects the graph at more than one point.

This problem involves determining if a graphed function is one-to-one using the horizontal line test. The graph shows a downward-opening parabola, and the solution explains why the function is not one-to-one. Suitable for students in Grades 9-12.

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