Sorry Mike just notice you have your getMyAssignments declared on the prototype. You are going to want to move it of the prototype definition so you can call it directly without creating a UserUtil object:
var UserUtil = Class.create();
UserUtil.prototype = {
initialize: function() {
},
type: 'UserUtil'
};
UserUtil.getMyAssignmentGroups = function(userID){
var queryString = "user=" + userID + "^group.typeLIKE52c230cd21412400abe30817dc6fb00f^ORtypeLIKEa59723f0213d6800abe30817dc6fb09d^ORtypeLIKE2da8677721056400abe30817dc6fb0fe";
var groupsArray = [];
var gr = new GlideRecord('sys_user_grmember');
gr.addEncodedQuery(queryString);
gr.query();
while (gr.next()) {
groupsArray.push(gr.group.toString());
}
return groupsArray;
},
