To determine whether each function is one-to-one, we need to apply the horizontal line test. A function is one-to-one if any horizontal line intersects its graph at most once.

Let's examine each graph:

1. Graph 1:
   The points are scattered, and multiple points lie on the same horizontal lines (e.g., at $y = 2$ and $y = 1$).
   Not one-to-one.

2. Graph 2:
   This graph represents a sinusoidal (wave-like) function. A horizontal line intersects this graph at more than one point in several places.
   Not one-to-one.

3. Graph 3:
   This is a straight line with a positive slope. Any horizontal line will intersect this graph exactly once.
   One-to-one.

4. Graph 4:
   This graph is a straight line with a negative slope. Like Graph 3, any horizontal line will intersect it exactly once.
   One-to-one.

5. Graph 5:
   This is a parabola opening upwards. A horizontal line drawn through the vertex or above/below the vertex will intersect the graph at two points.
   Not one-to-one.

6. Graph 6:
   The points are scattered again, and some horizontal lines intersect multiple points (e.g., at $y = 3$).
   Not one-to-one.

Summary of one-to-one:

• Graph 1: No
• Graph 2: No
• Graph 3: Yes
• Graph 4: Yes
• Graph 5: No
• Graph 6: No

Do you want further clarification on any graph, or would you like additional details?

Here are 5 related questions you could explore:

1. What is the horizontal line test, and why is it used for checking one-to-one functions?
2. How does the concept of inverse functions relate to one-to-one functions?
3. Can a function be one-to-one if it has a turning point?
4. Why are straight lines with non-zero slopes always one-to-one?
5. How does being one-to-one affect a function's domain and range?

Tip: For a function to have an inverse that is also a function, it must pass the horizontal line test, ensuring it is one-to-one!