I plan to send a book to someone as a graduation gift. I would like to include a card so they know it's from me and why they are getting it. I know that cards are considered First Class and books can be sent Media Mail. If I package them together, do I send the whole thing First Class, or can I put a First Class stamp on the card, attach it to the book, wrap it all up and send the whole thing as Media Mail. The extra weight of the card would not significantly increase the Media Mail cost, but I'd hate to have to pay First Class for the whole thing because it would be much more expensive.

I believe that the card can be considered an "invoice" in cases like this.  Media Mail rules allow for a short note or invoice to be included with the book that explains why the book was sent.  But you might want to check with your postmaster or clerk first, just to be sure.

Here's the relevant section from the DMM:

4.3 Written Additions
Markings that have the character of personal correspondence require, with certain
exceptions, additional postage at the First-Class Mail prices. The following written
additions and enclosures do not require additional First-Class Mail postage:
a. The sender’s and the addressee’s names, occupations, and addresses,
preceded by “From” or “To,” and directions for handling.
b. Marks, numbers, names, or letters describing the contents.
c. Words or phrases such as “Do Not Open Until Christmas” and “Happy Birthday,
Mother.”
d. Instructions and directions for the use of the item mailed.
e. A manuscript dedication or inscription not having the nature of personal
correspondence.
f. Marks to call attention to words or passages in the text.
g. Corrections of typographical errors in printed matter.
h. Manuscripts accompanying related proof sheets and corrections of proof
sheets including corrections of typographical and other errors, changes in the
text, insertions of new text, marginal instructions to the printer, and corrective
rewrites of parts.
i. Handstamped imprints, unless the added material is in itself personal or
converts the original matter to a personal communication.
j. Matter mailable separately as Standard Mail printed on the wrapper, envelope,
tag, or label.

The book can go media mail Carolyn, but IIRC anything along the lines of personal correspondence is not eligible for that rate.  Packing slips, invoices, etc. not "...not having the nature of personal correspondence" may be included in your media mail package. 

But do check with your PO, b/c I thought I heard it might be possible to add a letter and attach an additional .44 stamp for the first class (card) portion.  If it exists it's probably one of those regulations that are not well known, so check first :-)

I'm so confused right now I think I'll just bite the bullet, pay an extra dollar or so, and send the whole thing First Class. Thanks to all for your help!

Oh wait! I just saw "J" in Bernhard's list from the PO. Maybe I do just have to put an extra stamp on the card. I'll check with my friendly neighborhood Postmaster.

I was in the post office myself when this very subject came up and you cannot include the note without paying for 1st class.

It really is a "gray area" because it depends a lot on the actual content of the note, and how a particular person might view that note.  Since the OP said the note was to explain why the book is being sent and who it is coming from, it could reasonably be considered an invoice or packing slip, which is allowed under MM rates.  But, since it's also a gift, and the OP said "card", that could also reasonably be considered "personal correspondance" and be subject to first class rates.

ETA: I think on this one you could probably get three different postal inspectors to check the package and get three different opinions on what rates apply.