Is there an equation showing the change in the frequency of the cosmic background radiation over time?

I'm curious as to whether there was ever a time when the background radiation was in the visible spectrum. What frequency was it 300,000 years after the big bang when the universe first became transparent? And from the big bang up until 300,000 years, did that opaque haze which filled the universe change color/frequency, or would it have always been some shade of white or gray, varying only in brightness?