Owners and keepers are liable without a prior bite
Utah's dog statute, UCA 18-1-1, makes an individual who owns or keeps a dog liable for an injury caused by the dog, whether or not the dog is vicious or the owner knows it is. The official chapter text sets out the exceptions.
Damages follow UCA 78B-5-818, so your own fault reduces them. Summaries confirm Utah does not follow the one-bite rule.