The given graph represents a piecewise-defined function, and part of the function is already provided. Let's analyze each piece of the function:

1. For $x \leq -1$: The graph is a horizontal line at $y = 4$, so the function is constant: $f(x) = 4$ This is already correctly provided.

2. For $-1 < x \leq 2$: The function is linear, and the expression provided is $f(x) = 4 - x$, which is correct since this line has a slope of -1 (it decreases by 1 unit for each increase in $x$) and the y-intercept for this line appears to be 4.

3. For $x > 2$: The function becomes a horizontal line at $y = 1$. This means that for all values of $x > 2$, the function takes the value of 1.

Thus, the missing part of the piecewise function for $x > 2$ is: $f(x) = 1$

Final piecewise function: