1. The problem asks to find the value of $y$ for $y = f(1)$ using the graph of the function $f$.\n2. From the description, the graph has a local maximum near $(0,5)$, a local minimum near $(3,-5)$, and rises steeply afterward.\n3. To find $f(1)$, locate $x=1$ on the horizontal axis and find the corresponding $y$-value on the curve.\n4. Since $1$ is between $0$ and $3$, and the graph falls from about $5$ at $x=0$ to about $-5$ at $x=3$, the value at $x=1$ should be between these values, closer to the maximum side.\n5. Estimating from the graph, $f(1)$ is approximately $2$.\n6. Therefore, the nearest integer value for $y = f(1)$ is $2$.