A poorly bred mutt, can't tell what though... So no way of telling size, temperament, or anything. You're taking a big risk by not knowing what breed the dog is AND by taking a "free to good home" dog.
And see the area around her eyes? That's not healthy - could be a skin infection (possibly mange?) Maybe even chronic skin problems, which could be the actual reason for giving the dog away. Most "free to good home" dogs have medical or behavioral issues.
If you want the dog have them provide a vet statement saying that there is no skin infection (mange) and that the dog is 100% healthy. Then cross your fingers and hope it stays that way.
PS - Dogs aren't free. You DO have the money for it's supplies, monthly fees, and any emergencies... correct?