Yes, the graph does show a function.

Explanation: A graph represents a function if, for every value of $x$, there is only one corresponding value of $y$. This can be tested using the Vertical Line Test: if a vertical line drawn at any point on the graph intersects the curve at most once, then the graph represents a function.

In this case, no vertical line would intersect the red curve more than once at any given $x$-coordinate, which means this graph passes the Vertical Line Test and is therefore a function.

Would you like more details on this concept or have any questions?

Here are 5 related questions you might explore:

1. What is the Vertical Line Test, and why is it important in determining functions?
2. Can a graph fail the Vertical Line Test and still represent a relation?
3. How do you identify if a function is one-to-one using a horizontal line test?
4. What are the different types of functions, and how are their graphs different?
5. How do piecewise functions appear on a graph, and how do we test them for being functions?

Tip: Remember, every function has a unique $y$-value for each $x$-value, but not every relation is a function. Use the Vertical Line Test to quickly determine if a relation is a function.