Determine Functionality: Is This Graph a Function via the Vertical Line Test?

Is the given graph a function?

To determine if the given graph represents a function, we use the vertical line test: if any vertical line intersects the graph at more than one point, the graph is not a function.

Let's apply this test to the graph:

• Examine different sections of the graph by drawing imaginary vertical lines.
• Look for intersections where more than one point exists on the vertical line.

Upon examining the graph, we observe that there are several vertical lines that intersect the graph at multiple points, particularly in areas with loops or overlapping curves. This indicates that at those $x$-values, there are multiple $y$-values corresponding to them.

Since there exist such vertical lines, according to the vertical line test, the graph does not represent a function.

Thus, the solution to this problem is that the given graph is not a function.