to keep at

to continue: Thanks to everyone for keeping at it despite all the problems.

to keep in with

to maintain good relations with: We can’t afford to lose Jack as a client, so we’re going to have to keep in with him, despite how he treated Bob.

to keep off

to avoid talking about a particular subject: I think it best if we keep off the fees issue during the meeting.

to avoid consuming something: I’m keeping off meat at the moment.

to not walk on: Keep off the grass.

to keep on

to continue: I know it’s late, but we’ve got to keep on going until we’ve completed the draft.

to keep to

to stay within limits: We’ve got to keep to the EUR 25,000 budget.

to keep up with

to move at the same rate / stay up to date: If we don’t innovate we’re not going to keep up with the competition.

to key in

to enter information into a computer: You need to key in all the data into the form, then click send.

to knock (something) off

to stop working: I’m planning to knock off at around 5:30 this evening. So I’ll meet you in the pub at 6.

to produce something quickly: The manufacturers say they should be able to knock them off at a rate of about 100 an hour.

to reduce the price: They’ve knocked $20 off the price of all their tablets.

to knuckle down

to make a great effort: We’ve got a very tight deadline for this project so we’re all going to have to knuckle down.

to lay (somebody) off

to make employees redundant: BigCo laid off half of their marketing team yesterday.
The compound noun “layoff” means the action of making employees redundant.

to let (somebody) off

to not punish: The CEO must have known about the tax evasion, but the courts have let him off.

to live off

to use money earned: My salary isn’t much, but it’s enough to live off.

to live up to

to meet expectations: The site didn’t live up to expectations. I think we’ll have to look elsewhere.

to look into

to research: Bill – can you look into the tax aspects of this transaction?

to look out

to be careful: Apparently there are several permitting issues that we need to look out for before we go ahead with construction.

to look (something) over

to inspect: We looked over the site, and we don’t think it meets our requirements.

to look through

to read quickly: I looked through the contract last night. I’ll read it properly when I have time this afternoon.

to look (something) up

to consult a reference book or the internet: What’s the capital of Kiribati? Can somebody look it up?

to look up (intransitive verb)

to improve: Analysts are saying that the market should look up next year.