When you enable Facebook sharing of your FanExam responses you can customize how your website shows up.
To customize the information in the Facebook feed, like the preferred image and your website information, you need to set the Facebook Open Graph Protocol data. The Open Graph Protocol data are set on your own website in the form of html meta tags. This is quite technical, but some web publishing systems do this automatically for you.
Further information is available from Facebook in the sharing information for webmasters (look under Open Graph markup).