We replace x with x-1 to shift 1 unit to the right. This is because we're making each new input 1 smaller than the old input, which means we're moving the xy axis 1 unit to the left while keeping the f(x) curve fixed in place. That gives the illusion f(x) is moving 1 unit to the right.
The -1 at the end will subtract 1 from the y coordinate and shift everything down by 1 unit.
