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how to call a custom jquery function without attaching it to something

new to writing a function in jquery, just testing the waters.
I have this just to to demo:
(function ( $ ) {
$.fn.update_notifications = function( options ) {
// This is the easiest way to have default options.
var settings = $.extend({
// These are the defaults.
user_id: 0,
}, options );
alert('test');
};
}( jQuery ));
Which I include in a JS file included before the tag. What I want to know, is how to actually call it inside my html?
I was thinking something like:
<script type="text/javascript">
jQuery.update_notifications({
user_id: 1
});
</script>
But that tells me "jQuery.update_notifications is not a function"

You want to call it on selected element like this:
$("some_element").update_notifications();
You can find more here at the official documentation.

No, the function is not part of the jquery object, but of its fn child object
$.fn.update_notifications();
However, it doesnt make sense to add something to the jquery prototype if youre not doing sth jqueryobjectbased

To fix the issue you simply need to change $.fn.update_notifications to $.update_notifications. The $.fn namespace is used for attaching functions to instances of jQuery objects.
(function($) {
$.update_notifications = function(options) {
var settings = $.extend({
user_id: 0,
}, options);
console.log('test');
};
}(jQuery));
jQuery.update_notifications({
user_id: 1
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
That being said, your example is a little redundant as you've just wrapped the existing $.extend() function without adding any real logic - although I assume this is a work in progress.

If your function has nothing to do with any DOM elements, i would suggest you not to pollute jQuery. You can very well declare this function some where else (page, separate JS file etc.).
But if you still want to do this, you can try these
$.update_notifications();
or
$(window).update_notifications();
or
$(document).update_notifications();

Why are you exactly extending the Jquery object?
Usually, lacking a valid reason to do so you would simply write a function inside your script.
Let's assume you have a valid reason and proceed:
Once you bind your function to $ or better create object like $.custom and bind the function (and rest of custom things you wanna bind to Jquery) you can use it like a normal function - only prefix it with $.custom
Not sure I understand your question but are you searching how to run that function from HTML other than using jquery?
Are you asking for an example like this?
<p id="onThis" onclick="$.custom.yourFunctionName()">Click me.</p>
That is obtrusive JS code and is not best practice when dealing with Jquery.
You wanna bind that function to element with on or click handler when document is ready:
$(document).ready( function() {
$('#onThis').on('click', function here);
// OR //
$('#onThis').click(function here);
});
If there is no reason to bind it to jQuery, don't do it you are only implying to someone reading your code something that doesn't exist ;)

How to create events in javascript in order to send them to objects

I want to create some events in javascript, but what I want is to be able to use them with jQuery objects because I want to do a framework and it has to be easy to use.
What I want is something like this:
function myEvent() {//code here}
$("#myObject").myEvent()
And trigger the event there, of course I want to know how to get the object which triggered it because I can't do anything without it.
I think that I might have to extend a prototype, but I'm not sure about that.
Can anyone help me? Thank you!!

I think you mean custom methods. Events work differently in JavaScript then what your code is trying to display. You can extend jQuery functions like this:
jQuery.fn.extend({
check: function() {
return this.each(function() {
this.checked = true;
});
}
});
// Use the newly created .check() method
$( "input[type='checkbox']" ).check();
DOCS: https://api.jquery.com/jquery.fn.extend/

JoshSpears' answer is perfect. Check also this one, I think you'll find easier to implement (just C&P):
Assuming you have, for example:
var myEvent = function(str) {
alert(str);
};
And you want something like:
$('div').myEvent('hey guys!');
Just implement this:
$.fn['myEvent'] = function( options ) {
return this.each( function() {
myEvent(options);
});
};
This is just a simplification of the jquery plugin pattern wrapper. Check it out here:
https://github.com/jquery-boilerplate/jquery-boilerplate/blob/master/dist/jquery.boilerplate.js

why define function inside $()?

I came across a public JavaScript fragment that has the following lines of code:
$(function() {
var v1, v2;
v1 = new V1;
return v2 = new V2(v1);
});
The guts of the function are perfectly grokkable. But what is the significance of wrapping this in a $()?

$(fn) is a shortcut for $(document).ready(fn).

$(function() {...}); is a shorthand for $(document).ready(function(){...});
This means code inside will be executed as soon as DOM is ready. BTW its jquery syntax, there is no really pure javascript equivalent. It is not equivalent to window.onload = function(){...} which in jquery would be wrote: $(window).load(function(){...}); .
Don't be fooled by auto called anonymous function used in javascript:
(function(){...})()
or
(function(){...}())

$( fn ) is a shortcut for $(document).ready( fn ), which executes fn when the DOMContent is loaded.
In .ready docs you can see that these 3 are equivalent
$(document).ready(handler)
$().ready(handler) // this one is not recommended
$(handler)
With pure Javascript you could achieve the same behavior using
document.addEventListener("DOMContentLoaded", fn, false);
jQuery docs:
.ready
An example on jsFiddle

That notation is alias for $(document).ready(function() { ... });

How to create a jQuery function (a new jQuery method or plugin)?

I know that in JavaScript the syntax is as follows:
function myfunction(param){
//some code
}
Is there a way to declare a function in jQuery that can be added to an element? For example:
$('#my_div').myfunction()

From the Docs:
(function( $ ){
$.fn.myfunction = function() {
alert('hello world');
return this;
};
})( jQuery );
Then you do
$('#my_div').myfunction();

In spite of all the answers you already received, it is worth noting that you do not need to write a plugin to use jQuery in a function. Certainly if it's a simple, one-time function, I believe writing a plugin is overkill. It could be done much more easily by just passing the selector to the function as a parameter. Your code would look something like this:
function myFunction($param) {
$param.hide(); // or whatever you want to do
...
}
myFunction($('#my_div'));
Note that the $ in the variable name $param is not required. It is just a habit of mine to make it easy to remember that that variable contains a jQuery selector. You could just use param as well.

While there is a plethora of documentation / tutorials out there, the simple answer for your question is this:
// to create a jQuery function, you basically just extend the jQuery prototype
// (using the fn alias)
$.fn.myfunction = function () {
// blah
};
Inside that function, the this variable corresponds to the jQuery wrapped set you called your function on. So something like:
$.fn.myfunction = function () {
console.log(this.length);
};
$('.foo').myfunction();
... will flush to the console the number of elements with the class foo.
Of course, there is a bit more to semantics than that (as well as best practices, and all that jazz), so make sure you read up on it.

To make a function available on jQuery objects you add it to the jQuery prototype (fn is a shortcut for prototype in jQuery) like this:
jQuery.fn.myFunction = function() {
// Usually iterate over the items and return for chainability
// 'this' is the elements returns by the selector
return this.each(function() {
// do something to each item matching the selector
}
}
This is usually called a jQuery plugin.
Example - http://jsfiddle.net/VwPrm/

Yup — what you’re describing is a jQuery plugin.
To write a jQuery plugin, you create a function in JavaScript, and assign it to a property on the object jQuery.fn.
E.g.
jQuery.fn.myfunction = function(param) {
// Some code
}
Within your plugin function, the this keyword is set to the jQuery object on which your plugin was invoked. So, when you do:
$('#my_div').myfunction()
Then this inside myfunction will be set to the jQuery object returned by $('#my_div').
See http://docs.jquery.com/Plugins/Authoring for the full story.

$(function () {
//declare function
$.fn.myfunction = function () {
return true;
};
});
$(document).ready(function () {
//call function
$("#my_div").myfunction();
});

You can also use extend (the way you create jQuery plugins):
$.fn.extend(
{
myfunction: function ()
{
},
myfunction2: function ()
{
}
});
Usage:
$('#my_div').myfunction();

You can write your own jQuery plugins(function which can be called on selected elements) like below:
(function( $ ){
$.fn.myFunc = function(param1, param2){
//this - jquery object holds your selected elements
}
})( jQuery );
Call it later like:
$('div').myFunc(1, null);

Yes, methods you apply to elements selected using jquery, are called jquery plugins and there is a good amount of info on authoring within the jquery docs.
Its worth noting that jquery is just javascript, so there is nothing special about a "jquery method".

Create a "colorize" method:
$.fn.colorize = function custom_colorize(some_color) {
this.css('color', some_color);
return this;
}
Use it:
$('#my_div').colorize('green');
This simple-ish example combines the best of How to Create a Basic Plugin in the jQuery docs, and answers from #Candide, #Michael.
A named function expression may improve stack traces, etc.
A custom method that returns this may be chained. (Thanks #Potheek.)

You can always do this:
jQuery.fn.extend({
myfunction: function(param){
// code here
},
});
OR
jQuery.extend({
myfunction: function(param){
// code here
},
});
$(element).myfunction(param);

It sounds like you want to extend the jQuery object via it's prototype (aka write a jQuery plugin). This would mean that every new object created through calling the jQuery function ($(selector/DOM element)) would have this method.
Here is a very simple example:
$.fn.myFunction = function () {
alert('it works');
};
Demo

Simplest example to making any function in jQuery is
jQuery.fn.extend({
exists: function() { return this.length }
});
if($(selector).exists()){/*do something here*/}

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Define a function in jQuery</title>
<script src="https://code.jquery.com/jquery-3.5.1.min.js"></script>
<script>
$(document).ready(function() {
$.fn.myFunction = function() {
alert('You have successfully defined your function!');
}
$(".call-btn").click(function(){
$.fn.myFunction();
});
});
</script>
</head>
<body>
<button type="button" class="call-btn">Click Here</button>
</body>
</html>

how to combine jquery code into a javascript function

I need to add a jquery script into a javascript function and then call that function when #sortby is added to the url. Is this possible?
the jQuery
$("#myselect option[value='availability']").attr("selected","selected");
the Javascript
function sortBy(){
performanceQuery(perfpage);
tourQuery(tourpage);
return false;
}

$(window).on('hashchange', function() {
if (document.location.hash == '#sortby') sortBy();
});
function sortBy(){
$("#myselect option[value='availability']").prop("selected", true);
performanceQuery(perfpage);
tourQuery(tourpage);
return false;
}

jQuery is just a Javascipt library that provides some new functions (yes, this $ is just a funky name of a variable containing function). You can use it wherever you want.