Where to put my custom functions in WordPress?

I am pulling my hair out. I have created some simple functions that generate random numbers, pulled from a database that I want to use on wordpress pages. (And then call them from the theme files, such as header.php or page.php.)

I have tried putting the functions inside functions.php that is in the theme (as per the documentation I have read), but I keep getting the “call to undefined function” errors! What in the world am I doing wrong?

Example, here is a function inside the functions.php

function randomPollNumber() {
///this gets a random active poll number
    $sql12 = "SELECT id FROM poll WHERE removed = 0 AND active = 1 ORDER BY RAND() LIMIT 1";
    $result12 = mysql_query($sql12);
    $myrow12 = mysql_fetch_row($result12);
    $pollquestionid = $myrow12[0];
    return $pollquestionid;
}

And I am calling it, from the header.php file with this

<?php echo randomPollNumber(); ?>

And yes, I DID try using the if_function_exists, but of course it cannot FIND the function, so of course it does not exist. Please help?