在△ABC中，AC=BC=11，∠C=90°，点D在AC上，且AD = \frac{9}{2}，点P、Q同时从点D出发，以相同的速度分别沿射线DC、射线DA运动，以PQ为边向AC上方作正方形PQEF．当点P到达C点时，点Q同时停止运动，设PQ=x，正方形PQEF与△ABC重叠部分的面积为S．（1）填空；当点E在AB上时，PQ的长为3；（2）求S关于x的函数解析式，并直接写出自变量x的取值范围．---Diagram Description: - Type: Geometric diagram. - Main Elements: - A right-angled triangle ABC, with the right angle at vertex C. - Vertices are labeled A, B, C. - Side AC is drawn horizontally, and side BC is drawn vertically. - A rectangle FPEQ is inscribed within the triangle ABC. - Vertices P and Q of the rectangle lie on the side AC of the triangle. - Vertices F and E of the rectangle lie above AC. - Segment FP is perpendicular to AC (vertical line segment). - Segment EQ is perpendicular to AC (vertical line segment). - Segment FE is parallel to AC (horizontal line segment). - Point F is located on the side BC of the triangle. - Point E is located on the side AB of the triangle. - Points labeled C, P, D, Q, A are located on the line segment AC, approximately in that order from left to right. Point D is located on the segment PQ. (Note: The image provided only contains a geometric diagram. It does not contain the question stem, options, or any other accompanying text for a problem.)