WordPress shortcode with a switch

Yes, you can pass shortcode parameters wihtout values. They just appear on $atts with numeric keys. You can see this when you do var_dump($atts). One option to check their existance is then to use in_array().

function info( $atts ) {
    // check if extended is passed in $atts with or without value
    $extended = isset( $atts['extended'] ) ? $atts['extended'] : in_array( 'extended', $atts );

    if ( $extended ) {
        // do something
    }

    // more code
}