1. The problem asks for the value of the function $f$ at $x=4$, i.e., $f(4)$. 2. From the graph, we identify the point where $x=4$. This corresponds to point D with coordinates $(4,1)$. 3. The value of the function at $x=4$ is the $y$-coordinate of point D, which is $1$. 4. Therefore, $f(4) = 1$. 5. The correct answer is option C: 1.