This work presents a framework for a robot with a multi-fingered hand to freely utilize daily tools, including functional parts like buttons and triggers. An approach heatmap is generated by selecting a functional finger, indicating optimal palm positions on the object's surface that enable the functional finger to contact the tool's functional part. Once the palm position is identified through the heatmap, achieving the functional grasp becomes a straightforward process where the fingers stably grasp the object with low-dimensional inputs using the eigengrasp. As our approach does not need human demonstrations, it can easily adapt to various sizes and designs, extending its applicability to different objects. In our approach, we use directional manipulability to obtain the approach heatmap. In addition, we add two kinds of energy functions, i.e., palm energy and functional energy functions, to realize the eigengrasp. Using this method, each robotic gripper can autonomously identify its optimal workspace for functional grasping, extending its applicability to non-anthropomorphic robotic hands. We show that several daily tools like spray, drill, and remotes can be efficiently used by not only an anthropomorphic Shadow hand but also a non-anthropomorphic Barrett hand.