Yes of course you can extend it. Class DbFunctions only contains code that helps the provider of your IQueryable to translate the expression into SQL.
An IEnumerable holds all code to create an Enumerator for you upon request. The Enumerator represents a sequence. Upon request it will give you the first element of the sequence, and once you've got an element it will give you the next one (provided there is one).
An IQueryable works differently. Usually an IQueryable is not meant to be performed by your process, but for instance a database, a remote web site, a CSV file controller, etc.
That is why you need to tell an object that produces IQueryables for which process it must create the IQueryable. In case of Entity Framework you inform the DbContext which database to use.
The IQueryable object holds an Expression to be performed and a Provider. The provider knows which process will perform the query. It also knows how to translate the Expression into the format that the other process understands. Quite often this will be SQL.
If you investigate the remarks section of the MSDN descriptions of IQueryable functions like Where, GroupBy, Select, you'll see that most of these functions will only change the Expression.
As long as you don't ask for the Enumerator, usually implicitly by asking for the first element of a sequence, like in ToList, foreach, FirstOrDefault, etc, the Provider has nothing to do.
But once you ask for the Enumerator, the Expression will be translated by the Provider, who will use the translation to query the data from the other process and create an Enumerator object that can give you the first element of the sequence, and the next ones.
DbFunctions are used when the Provider translates the Expression into SQL. If you create a Queryable with DbFunctions and in your debugger look at the created Expression, you'll still find the used DbFunctions.
The DbFunctions only translate the input into SQL. If does not perform the query itself. The translation is done in local memory.
Having understood this, you can use any function as long as it only changes the Expression into new Expressions into formats that your provider understands.
This means you can't use any of your own functions, or classes. There are even several LINQ functions you can't use
See supported and non-supported LINQ methods
However, if your extension functions input an IQueryable and output an IQueryable, then your extension function will only change the Expression. As long as you fill the Expression with supported LINQ methods you're fine
So if you want to extend IQueryable with a function that returns an IQueryable containing only the invoice that are due to day:
public static IQueryable<Invoice> WhereDueToday(this IQueryable<Invoice> invoices)
{ // returns all invoices that must be paid today
return invoices
.Where(invoice => DbFunctions.TruncateTime(invoice.DueDate) == DateTime.Today);
}
Usage:
IQueryable<Invoice> invoices = dbContext.Invoices
.Where(invoice => ..);
IQueryable<Invoice> invoicesDueToDay = invoices
.WhereDueToday();