cater for 是短语,意思是“满足”,用法有 cater for sb./sth.
satisfy是及物动词,意思也是“满足”还有“消除,清偿（债务）,履行,赔偿”的意思 其形容词形式是satisfying,其副词的形式是satisfyingly
live up to 也是短语,意思是“实践,做到,与.相配”,用法有live up to sth.