As mentioned by Quynh Nguyen, you don't need the '.' in the className. However - document.getElementsByClassName('col1') will return an array of objects.
This will return an "undefined" value because an array doesn't have a class. You'll still need to loop through the array elements...
function changeBGColor() {
var cols = document.getElementsByClassName('col1');
for(i = 0; i < cols.length; i++) {
cols[i].style.backgroundColor = 'blue';
}
}