英语翻译Billie Holiday’s reputation as a great jazz-blues singer

你应该查rest on的意思
断句是这样的
1.Billie Holiday’s reputation
2.as a great jazz-blues singer
3.rests on her ability to give emotional depth to her songs.
rest on
1.搁在〔支撑在〕…上
2.依赖于,寄托于…上,基于
3.接触到; 达到; 朝向; (使)落在…上 1.搁在〔支撑在〕…上
The bridge rests on stone arches.
这座桥由石拱支撑.
Her head rested on one of her hands as she sat there waiting.
她一只手托着头,坐在那儿等候.
2.依赖于,寄托于…上,基于
Your success rests on your efforts.
你的成功有赖于你的努力.
His argument does not rest on reasoning or on experiment,but on authority.
他的论点不是依靠推理或者实验,而是靠权威.
We rest our hopes on you.
我们把希望寄托在你们身上.
3.接触到; 达到; 朝向; (使)落在…上
His eyes rested on the peaceful valley below.
他的目光落在下面宁静的山谷中.
It's good to rest one's eyes on such a beautiful view.
观看这样的美景使人赏心悦目.

Billie Holiday’s reputation as a great jazz-blues singer rests on her ability to give emotional depth to her songs.
singer rests不是一个词语
singer单独翻译为歌手 rest on 才是一个词组 意思为“依靠、依赖于”
随意应该在sing...

这句的主语是Billie Holiday’s reputation , as a great jazz-blues singer 在此做了singer的定语限定了它，rest 指“位于。。。或在于。。。”，你的翻译里它翻译成了“建立在。。。”

Billie Holiday’s reputation as a great jazz-blues singer rests on her ability to give emotional depth to her songs.
rests on 这应该是一个短语，此处翻译为建立在。。。