filter an SQL table based on user input, without refreshing the page using PHP and pure JS AJAX [on hold]

let's assume I have a table with a number of products, say:

+--------------------+------------+---------------+---------------+
|    Product_Name    | product_id | Product_Price | Product_Store |
+--------------------+------------+---------------+---------------+
| Intel core i5-8500 | Ee358KEjKi |           225 |             8 |
| AMD Ryzen 5 2600X  | 1SWOrA2JXY |           200 |             3 |
+--------------------+------------+---------------+---------------+

the list of products is printed to the user, and I want the user to be able to filter it by certain things, for example he'd be able to filter by price range, or filter by store.

Doing it with PHP and html isn't a problem if I don't mind the page to be refreshed or redirected, but I don't want it to do any of that, I want the table to get updated live as the user marks the checkbox with his preferred store, or when he enters the price range he wishes for. I guess this is where AJAX comes to play, which i'm not at all familiar with. I'd appreciate an example of using AJAX (with pure js, no jquery) for this purpose, so i'll know how to implement it in my own project.

Thank you very much.