Fatal error: Call to a member function prepare() on a non-object with PDO

I have a file that includes another file:

index.php is a dynamic template

<?php
    $db = new PDO("mysql:host=localhost;dbname=db", $DB_USER, $DB_PASSWORD);
    include(functions.php);
?>

functions.php

<?php
    $preparedStatement = $db->prepare("SELECT id FROM table LIMIT 1");
    $preparedStatement->execute();
    $firstId = $preparedStatement->fetchAll();
?>

when functions.php executes I get:

Fatal error: Call to a member function prepare() on a non-object

at line

$preparedStatement = $db->pre开发者_JAVA技巧pare("SELECT id FROM table LIMIT 1");

What is wrong with this code such that it throws the error?

Edit: The error arose from me connecting directly the the functions.php file, it did not appear when it was included from index.php, the problem I had was content not loading in later inclusions, that was caused by me forgetting to properly address arrays in a later included file. The selected answer is correct for the question I presented.

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inclusion of files is wrong;

include index.php on function.php page only , dont include vice versa

best practice to use include_once