To determine if the graph represents a function, we can once again use the Vertical Line Test.

In the provided graph, we see a circle centered at approximately $(-1, 0)$.

Applying the Vertical Line Test:

If you draw a vertical line through any x-value on this graph, the line will intersect the circle at two points.

For example:

• A vertical line at $x = -1$ will intersect the circle at two points (one above and one below the center).

Conclusion:

Since there are vertical lines that intersect the graph at more than one point, this graph does not represent a function.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this topic:

1. What is the equation of a circle, and how does it relate to functions?
2. Can a circle ever represent a function? Why or why not?
3. How do other conic sections (like ellipses, parabolas, and hyperbolas) relate to functions?
4. What are the general properties of functions regarding their graphs?
5. How does the concept of one-to-one functions differ from general functions?

Tip: Always remember that for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).