Hi there,
If you're not planning on getting an internal transfer flight from Narita to Tottori and will travel there by train doing sightseeing on the way, then a good starting point it to compare the price of individual tickets with the price of a 7 day rail pass: ¥28,300.
Travel by JR trains from Narita to Tottori comes in at just over ¥20,000. This means that you'd have to do an additional ¥8,000 of JR travel to make a Japan Rail Pass worthwhile over just buying single tickets.
If you have 7 days, you could make your trip down via Takayama/Kanazawa, or plan on a trip to Miyajima/Hiroshima. At this point a 7 day rail pass would be worthwhile - it very much depends on how much additional travel you plan on doing en route.
You can look up train timetables and costs for all of your legs at the Hyperdia travel planning website and learn how to use Hyperdia for Japan Rail Pass holders through our video blog.
Hope this helps!