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To determine whether each graph represents a one-to-one function, we apply the **horizontal line test**. If any horizontal line drawn across the graph intersects the function more than once, then the function is **not** one-to-one. Let's analyze each graph:

1. **Graph 1**:
   - This graph shows a set of points, which suggests a relation but not necessarily a function.
   - Since multiple points share the same y-values, it is **not one-to-one**.

2. **Graph 2**:
   - This is a sinusoidal curve, which fails the horizontal line test (horizontal lines will intersect the graph more than once).
   - Therefore, it is **not one-to-one**.

3. **Graph 3**:
   - This graph is a straight line with a positive slope, and no horizontal line intersects it more than once.
   - This is a **one-to-one** function.

4. **Graph 4**:
   - This graph consists of distinct points, but because the same y-value is repeated for different x-values, it fails the horizontal line test.
   - It is **not one-to-one**.

5. **Graph 5**:
   - This is a parabola opening upward, which clearly fails the horizontal line test because horizontal lines will intersect it twice.
   - Thus, it is **not one-to-one**.

6. **Graph 6**:
   - This graph contains scattered points, with different x-values sharing the same y-values. It does not pass the horizontal line test.
   - Therefore, it is **not one-to-one**.

In summary, the only one-to-one function is **Graph 3**. 

Would you like further clarification on the horizontal line test or any other details?

Here are 5 related questions to explore:
1. What makes a function one-to-one?
2. How can you algebraically verify if a function is one-to-one?
3. What is the difference between one-to-one functions and onto functions?
4. Can a parabolic graph ever be one-to-one?
5. How do inverse functions relate to one-to-one functions?

**Tip**: Always use the horizontal line test to quickly determine if a function is one-to-one visually!

For each function graphed below, state whether it is one-to-one.

Analyze various graphs to determine if the function is one-to-one using the horizontal line test. Learn about key mathematical concepts such as functions and the criteria for one-to-one functions. This content is ideal for students in Grades 9-11.

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