What is <*> called and what does it do?

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How do these functions in the Applicative typeclass work?

(<*>) :: f (a -> b) -> f a -> f b
(*>)  :: f a -> f b -> f b
(<*)  :: f a -> f b -> f a

(That is, if they weren't operators, what might they be called?)

As a side note, if you could rename pure to something more friendly to non-mathematicians, what would you call it?

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