Hello everyone,

I have a small question which is bothering me a lot.

I was learning in my precalculus book about the shifting of of functions and it tells me about the function

i understand that it is compressed by a factor of 1/2 and it is shifted 1 unit to the right .

but I still can't wrap around my head the actual concept.

Why subtracting moves it to the right, rather than adding?

and most of all I'm having trouble understanding how can the -1 affect it at all, how could it stay a constant effect rather than affecting the x value?