Insert a wordpress page with a function/plugin
I am creating a wordpress plugin and now I want to make an ajax call. For now I follow this method.

1. I create a page through wordpress dashboard
2. Create a new Template file
3. Put my PHP function in that template file
4. Assign that template to my new page.

So My ajax url is like that
http://mywordpresssite/custom_ajax
(This basically is a wordpress page but since it has a custom template selected so When I send an ajax request to this I works for me)

Now My question

I am actually tired of creating wordpress page and applying templates. Moreover my plugins are not plugnplay since I need to create template in theme folder. And if accidently someone delete that custom_ajax page from the dashboard or trash then my functionality breaks. 

Is there a way to create a page (or link) through my plugin and then I put my custom function in it so If somene go to that link it actually accessing my custom function(like Code Igniter do it). My question is not specifically about ajax, I know wordpress has another way to deal with ajax but I only want to know that Is it possible to create a page or link through a plugin and point it to a  custom function of plugin. 
Insert a wordpress page with a function/plugin
===

I am creating a wordpress plugin and now I want to make an ajax call. For now I follow this method.

1. I create a page through wordpress dashboard
2. Create a new Template file
3. Put my PHP function in that template file
4. Assign that template to my new page.

So My ajax url is like that
http://mywordpresssite/custom_ajax
(This basically is a wordpress page but since it has a custom template selected so When I send an ajax request to this I works for me)

Now My question

I am actually tired of creating wordpress page and applying templates. Moreover my plugins are not plugnplay since I need to create template in theme folder. And if accidently someone delete that custom_ajax page from the dashboard or trash then my functionality breaks. 

Is there a way to create a page (or link) through my plugin and then I put my custom function in it so If somene go to that link it actually accessing my custom function(like Code Igniter do it). My question is not specifically about ajax, I know wordpress has another way to deal with ajax but I only want to know that Is it possible to create a page or link through a plugin and point it to a  custom function of plugin. 