What is the "hasClass" function with plain JavaScript?

You can check whether element.className matches /\bthatClass\b/.
\b matches a word break.

Or, you can use jQuery's own implementation:

var className = " " + selector + " ";
if ( (" " + element.className + " ").replace(/[\n\t]/g, " ").indexOf(" thatClass ") > -1 ) 

To answer your more general question, you can look at jQuery's source code on github or at the source for hasClass specifically in this source viewer.

Simply use classList.contains():

if (document.body.classList.contains('thatClass')) {
    // do some stuff
}

Other uses of classList:

document.body.classList.add('thisClass');
// $('body').addClass('thisClass');

document.body.classList.remove('thatClass');
// $('body').removeClass('thatClass');

document.body.classList.toggle('anotherClass');
// $('body').toggleClass('anotherClass');

Browser Support:

• Chrome 8.0
• Firefox 3.6
• IE 10
• Opera 11.50
• Safari 5.1

classList Browser Support