Is there a way in PHP to limit an image to only be displayed on the home page(index.php).

Simple, put a variable in the session, or a cookie on the user's browser to indicate if this is the first view of the page or not.

Um, well if you're using header/footer files and you don't want to make an exception for index.php, you could just add:

<?php
if ($_SERVER['REQUEST_URI'] == '/index.php') echo '<img src="index-image.jpg" />';
?>