Should both video cards be displaying a signal to my monitor?

I’ve had this computer so long. I can’t remember if my monitor used to work on either video card or if it’s always just been the one on the right. Currently if I plug my monitor into the video card on the left in any port, I have no display on my monitor. It will only work if I plug it into the right. Is that how it’s supposed to go when you have two video cards? Or is something wrong?