To determine whether the graphs pass the Horizontal Line Test, you need to check if you can draw a horizontal line that intersects the graph more than once:

1. Graph 1: Yes

   • A horizontal line can only intersect this graph at one point, so it's impossible to draw a horizontal line that intersects the graph more than once.

2. Graph 2: Yes

   • Similarly, any horizontal line will only intersect this graph at one point.

3. Graph 3: No

   • This graph is a sine wave, so a horizontal line can intersect the graph at multiple points.

4. Graph 4: No

   • This graph consists of multiple distinct points, and a horizontal line can intersect more than one of these points.

5. Graph 5: No

   • A horizontal line can intersect more than one of the points on this graph.

6. Graph 6: Yes

   • A horizontal line will intersect this line graph at only one point.

Summary:

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

Would you like further explanation on any of these graphs?

Here are five related questions for you to consider:

1. What does it mean for a function to be one-to-one?
2. How does the Horizontal Line Test relate to the concept of inverse functions?
3. Can a function pass the Vertical Line Test but fail the Horizontal Line Test?
4. How would the graphs change if they represented different types of functions (e.g., quadratic, cubic)?
5. How can the Horizontal Line Test help in understanding real-world problems modeled by functions?

Tip: Remember, a function passes the Horizontal Line Test if and only if it is injective, meaning each output (y-value) is associated with exactly one input (x-value).