An analysis of the direct correlation functions c_{ij}(r) of binary additive hard-sphere mixtures of diameters σ_{s} and σ_{b} (where the subscripts s and b refer to the "small" and "big" spheres, respectively), as obtained with the rational-function approximation method and the WM scheme introduced in previous work [S. Pieprzyk et al., Phys. Rev. E 101, 012117 (2020)2470-004510.1103/PhysRevE.101.012117], is performed. The results indicate that the functions c_{ss}(r<σ_{s}) and c_{bb}(r<σ_{b}) in both approaches are monotonic and can be well represented by a low-order polynomial, while the function c_{sb}(r<1/2(σ_{b}+σ_{s})) is not monotonic and exhibits a well-defined minimum near r=1/2(σ_{b}-σ_{s}), whose properties are studied in detail. Additionally, we show that the second derivative c_{sb}^{''}(r) presents a jump discontinuity at r=1/2(σ_{b}-σ_{s}) whose magnitude satisfies the same relationship with the contact values of the radial distribution function as in the Percus-Yevick theory.