Techniques for generic object recognition, which targets everyday objects such as cups and spoons, and techniques for approach vector estimation (e.g. estimating grasp position), which are needed for carrying out tasks involving everyday objects, are considered necessary for the perceptual system of service robots. In this research, we design feature for generic object recognition so they can also be applied to approach vector estimation. To carry out tasks involving everyday objects, estimating the function of the target object is critical. Also, as the function of holding liquid is found in all cups, so a function is shared in each type (class) of everyday objects. We thus propose a generic object recognition method that can estimate the approach vector by expressing an object's function as feature. In a test of the generic object recognition of everyday objects, we confirmed that our proposed method had a 92% recognition rate. This rate was 11% higher than the mainstream generic object recognition technique of using convolutional neural network (CNN).