Pass widget variable to external function

Not sure if this should be moved to WP-Advanced or not, but here it goes.

I am working on a custom widget which displays posts from a selected taxonomy (category or tag). This widget contains a textbox which the user enters an ID of a taxonomy (category or tag) to exclude from posts. This ID can vary from widget to widget as multiple instances of this widget will appear on the same page. I am looking for a way to pass the $exclude variable from widget() to the excludeTheID()function which is located in functions.php

For the sake of this example, here is a mock of what I am trying to accomplish:

class testWidget extends WP_Widget {

    public function __construct() {
        // .......
    }

    public function form( $instance ) {
        // This widget contains a text field ($exclude)  that the user is to enter a taxonomy ID into.
    }

    public function update( $new_instance, $old_instance ) {
        // .......
    }

    public function widget( $args, $instance ) {
        // this value represents what the user would enter in the textbox of the widget
        $exclude = 15;
        // .......

        // This function does the work
        add_filter( "posts_where", "testFunction" );    

        // Create a new query
        $loop = new WP_Query();

        // Remove the filter
        remove_filter( "posts_where", "testFunction" );
    }
}

// In Functions.php: External function responsible for generating the new WHERE clause using the  value in $exclude.

function excludeTheID( $where, $exclude )
{   

    $clauses = array(
        array(
            'taxonomy'  => 'category',
            'field'     => 'id',
            'terms'     => $exclude,
            'operator' => 'NOT IN',
        ),
    );

    // Access the global WordPress DB variable
    global $wpdb;

    // Create the new WHERE Query string using the above arrays
    $tax_sql = get_tax_sql( $clauses, $wpdb->posts, 'ID' );
    $where .= $tax_sql['where'];

    return $where;
}

I do not want to use globals to accomplish this as each widget will be passing a unique value for $exclude in every instance of that widget on a page.

Any guidance would be greatly appreciated ??

Thanks.