For limited distortion source coding, it is generally considered that the minimum value of the coding average distortion is 0, and the maximum value is the minimum distortion value of making R(D) = 0. This is the definition domain of the information rate distortion function. In this paper, the upper and lower bounds of the information rate distortion function R(D) are derived and computed for the typical sources. The results show that the lower bound of the coding average distortion D is related to the symbol distortion function, which can further improve the theory of limited distortion source coding.