To determine the $y$-value of the function when $x = -2$, locate $x = -2$ on the horizontal axis and identify the corresponding point on the graph. From the image:

1. At $x = -2$, the point lies at $y = 4$.

Thus, the $y$-value is $4$.

Would you like further clarification or have additional questions? Here are some related queries to consider:

1. What is the $y$-value of the function when $x = 3$?
2. Are there any $x$-values that have the same $y$-value as $x = -2$?
3. Can we determine the function's behavior for $x > 5$?
4. Is this function a one-to-one function, and why?
5. How can we interpret the domain and range of the function based on the graph?

Tip: When analyzing graphs, always check for clear coordinates and align values precisely with the axes for accuracy.