An authority created by a governmental unit exempt from the referendum requirement of § 15.2-5403 is hereby declared to be performing a public function on behalf of the governmental unit that is the sole member of such authority with respect to which the authority is created and to be a public instrumentality of such governmental unit. Accordingly, an authority created by a governmental unit exempt from the referendum requirement of § 15.2-5403 shall be exempt from state and local taxation to the same extent that the governmental unit that is the sole member of such authority is exempt from such taxation.