Alice asks: "A few days ago, I drove from Vonore to Greenback onto 321 and saw the most glorious rainbow I have ever seen, but I'm confused because it was in the west. That's not right, I thought. My mother always said to look for the rainbow in the east! I want to know are they rare, and if so, then why?"
Interesting question Alice! What you're talking about, morning rainbows, are somewhat rare.
For the most part, we're most likely to see rainbows in the afternoon.
Rainbows are caused by the splitting of white sunlight into the component colors by raindrops. Some of that light enters the drop, causing the color components of the sunlight to be bent by different amounts depending upon their wavelength.
We see the different wavelengths as different colors. Then, the different colors reflect off the backside of the drop, and when they pass through the front of the drop again, they are bent once again.
Now, here's a rule: A rainbow is always directly opposite the sun from the observer's perspective. This explains why rainbows are only seen when the sun is low in the sky-- that's usually in late afternoon.
However, in rare cases, that happens in the early morning, in which case the rainbow will be see to the east, just like you saw Alice.
So the answer-- morning rainbows are rare, but they're formed in the same way as rainbows seen during other times of the day.