The task asks to select all graphs that represent $y$ as a function of $x$. To determine if a graph represents a function, we apply the vertical line test. This test states that if any vertical line intersects the graph at more than one point, the graph does not represent $y$ as a function of $x$.

Let's examine each of the six graphs from the image:

1. Top left: This graph has a curve where, at some points, a vertical line would intersect the curve in more than one place. Therefore, this is not a function.

2. Top center: This is a horizontal line. A vertical line will intersect the graph at exactly one point for any $x$-value. Therefore, this is a function.

3. Top right: This graph is a slanted straight line. Again, any vertical line intersects the graph at exactly one point. Therefore, this is a function.

4. Bottom left: This graph is a curve (possibly a polynomial). A vertical line would intersect the graph at exactly one point for any $x$-value. Therefore, this is a function.

5. Bottom center: This is another curve that also passes the vertical line test (no vertical line intersects it at more than one point). Therefore, this is a function.

6. Bottom right: This graph features a circle. A vertical line will intersect the graph at two points in several places. Therefore, this is not a function.

Conclusion:

The graphs that represent $y$ as a function of $x$ are:

• Top center (horizontal line)
• Top right (slanted line)
• Bottom left (polynomial-like curve)
• Bottom center (another curve)

Would you like further details or explanations on any of these concepts?

Related questions:

1. What is the formal definition of a function?
2. How does the vertical line test relate to function theory?
3. Why is a circle not considered a function?
4. What are examples of real-world phenomena that can be modeled by functions?
5. How do we differentiate between injective, surjective, and bijective functions?

Tip:

Always apply the vertical line test when in doubt about whether a graph represents a function. If a vertical line crosses the graph more than once, it's not a function!