If your business meets the definition of a customary home occupation in (item 41in Chapter 9, Section 9.3 of the Unified Development Code), generates no unusual traffic, uses no on-site employees, and does not create a nuisance for adjoining property owners, then yes.
The definition reads:
Customary home occupation shall mean an occupation customarily carried on in the home by a member of the occupant’s family without structural alteration in the building or any of its rooms and without the installation of machinery other than that customary to normal household operation or additional equipment, provided that no person other than a member of the family of the owner or user of the principal single-family dwelling shall be employed or work in or at such home occupation. A customary home occupation shall not include the physical or medical treatment of persons or animals, professional services, business services, barber shops, beauty shops, dance studios, carpenter shops, electrical shops, plumber shops, radio shops, auto repairing or painting, furniture repairing or sign painting.