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We analyze the bivariate distribution, in color versus absolute magnitude (u-r vs. Mr), of a low-redshift sample of galaxies from the Sloan Digital Sky Survey (2400 deg2, 0.004 < z < 0.08, -23.5 < Mr < -15.5). We trace the bimodality of the distribution from luminous to faint galaxies by fitting double Gaussians to the color functions separated in absolute magnitude bins. Color-magnitude (CM) relations are obtained for red and blue distributions (early- and late-type, predominantly field, galaxies) without using any cut in morphology. Instead, the analysis is based on the assumption of normal Gaussian distributions in color. We find that the CM relations are well fitted by a straight line plus a tanh function. Both relations can be described by a shallow CM trend (slopes of about -0.04, -0.05) plus a steeper transition in the average galaxy properties over about 2 mag. The midpoints of the transitions (Mr = -19.8 and -20.8 for the red and blue distributions, respectively) occur around 2 × 1010 M⊙ after converting luminosities to stellar mass. Separate luminosity functions are obtained for the two distributions. The red distribution has a more luminous characteristic magnitude and a shallower faint-end slope (M* = -21.5, α -0.8) compared to the blue distribution (α ≈ -1.3, depending on the parameterization). These are approximately converted to galaxy stellar mass functions. The red distribution galaxies have a higher number density per magnitude for masses greater than about 3 × 1010 M⊙. Using a simple merger model, we show that the differences between the two functions are consistent with the red distribution being formed from major galaxy mergers.