I need to write test cases for a function which has $ as argument. But the $ argument is being used as a function and an object

function test($, sf) {
    let resultObj = {}
    resultObj.id = setTimeout(function () {
        $.ajax({
            'url': URL,
            'type': 'GET',
            'success': function (response) {
            },
            'error': function () {
            }
        });
    })

    $(document).ready(function () {
        $(document).ajaxSend(function () {
           
        })
    });
    return {
        start: function (options) {
            resultObj.id(options);
        }
    }

}

i tried test case like this

import * as test from './function'

test((doc) => {
    return {
        ready: (cb) => { cb() },
        ajaxSend: (cb) => { cb() }
    }
})
describe("test suite", () => {

    test("testing ", async () => {

    });

});

How can i mock $ as both function and object