
Brandon B. answered 03/02/21
Physics PhD. 10+ years teaching trig based physics.
To stretch a function f(x) by a factor h we simply multiply hf(x). To shift a function right by an amount b we want the value of f(a) at x = a to instead be at x = a + b. This means f(x) → f(x-b), since f(a+b-b) = f(a).