1. The problem asks to find the value of $y$ for the function $f$ at $x = -2$, i.e., find $f(-2)$. 2. From the graph description, at $x = -2$, the function $f$ is on the rising left side near the local maximum and the approximate $y$-value is about 5. 3. Since the problem asks for the nearest integer, we round the approximate value $5$ to the nearest integer, which is $5$. 4. Therefore, the value of $y$ when $x = -2$ is $5$.