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!