The Four Corners region is littered with petroglyph sites like this. There a several along the Colorado near Moab and more near Blanding and Monticello. It's fairly easy to scratch an image into the desert varnish on these rocks and in a sheltered area it will last for hundreds of years. About the only way the images can be dated is to look for horses. If you see an image of a horse you know that was done sometime after 1600 when the Spanish came north.
Atlatl Rock in the Valley of Fire State Park northeast of Las Vegas
Pictographs (rock painting) in a small alcove with a spring in Canyonlands National Park (not far from Newspaper Rock)
Along the Colorado River near Moab
Also near Moab