Example: I took up that job offer.
For more meanings of the phrasal verb take up
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(informal) arrive; turn up
Example: What time are you going to rock up tonight?
attracted the attention
Example: Her performance caught the eye of the producer.
taking the least hopeful view; the worst thing that can happen is
Example: You might as well buy a lottery ticket - at best you win a million dollars and at worst you've wasted only a few dollars.