Question

I wonder how I can write the jQuery is method using only javascript?

You can’t use any third party libraries. Only the javascript provided from the browser.

FYI the method is in jQuery:

Check the current matched set of elements against a selector, element,
or jQuery object and return true if at least one of these elements
matches the given arguments.

Answer 1

If you need support for older browsers, you should use jQuery. This should work in IE9, Firefox and Chrome.

//returns true if element matches selector or if element is equal to the node passed as selector
function is( elem, selector ) {
    var div = document.createElement("div");
    var matchesSelector = div.webkitMatchesSelector || div.mozMatchesSelector || div.msMatchesSelector;
    return typeof selector == "string" ? matchesSelector.call( elem, selector ) : selector === elem;
}
//returns true if any elements in the array/nodelist "is" selector
function anyIs( elems, selector ) {
    var l = elems.length, i;

    for( i = 0; i < l; ++i ) {
        if( is( elems[i], selector ) ) {
            return true;
        }
    }
    return false;
}

is(document.createElement("div"), "div")
//true
is(document.createElement("div"), "li")
//false
anyIs(document.getElementsByTagName("div"), document.getElementsByTagName("div")[3])
//true
anyIs(document.getElementsByTagName("div"), "div")
//true