1. **State the problem:** Given a point $(m,n)$ on the graph of $y = f(x)$, find the corresponding point on the graph of $y = f(x - 11) + 4$. 2. **Recall the transformation rules:** - The function $y = f(x - 11)$ represents a horizontal shift of the graph of $f(x)$ to the right by 11 units. - The function $y = f(x - 11) + 4$ represents the above horizontal shift plus a vertical shift upward by 4 units. 3. **Apply the horizontal shift:** - Since the graph shifts right by 11, the $x$-coordinate of the point changes from $m$ to $m + 11$. 4. **Apply the vertical shift:** - Since the graph shifts up by 4, the $y$-coordinate changes from $n$ to $n + 4$. 5. **Write the new point:** - The point on the transformed graph is $(m + 11, n + 4)$. 6. **Check the options:** - The correct choice is $(m + 11, n + 4)$. **Final answer:** $(m + 11, n + 4)$