Web API 2 REST Service Advanced Data Filtering

My team has currently implemented a REST API (JSON) using the Web API 2 platform for .NET. We have some working URLs, such as:

/api/schools 
/api/schools/5000 
/api/occupations 
/api/occupations/22

And here is some of our data controller code:

public class OccupationsController : ApiController
{
    // /api/Occupations/1991
    public IHttpActionResult GetOccupation(int id)
    {
        var occupation = GetAllOccupations().FirstOrDefault((p) => p.OccupationID == id);
        if (occupation == null)
        {
            return NotFound();
        }
        return Ok(occupation);
    }
    // /api/occupations
    public IEnumerable<Occupation> GetAllOccupations()
    {
        var ctx = new TCOSDBEntities();
        return ctx.Occupations.OrderBy(occupation => occupation.Title);          
    }

}

We are now introducing data filtering (based on user checkbox selection) and I am curious how to approach this in our existing API, or if I should abandon REST for filtering down and try a different approach all together?

Here is our checkbox filtering mechanism: Checkbox UI

How can I introduce search parameters in my REST services and DataController methods? Like, how do I get a range filter on a field (like Cost?)? Can I have multiple fields filtering, like Cost, Tuition, etc?