If c > 0, then f(x - c) is a shift of f(x) by c units to the right, and f(x + c) is a shift by c units to the left.
If d > 0, then f(x) - d is a shift by d units downward, and f(x) + d is a shift by d units upward.
Let g(x) = x. Then f(x) = g(x + a) - b = (x + a) - b. So to get g(x), we translate f(x) to the left by a units, and down by b units.
Note that we can also interpret the translation as
• a shift upward of a - b units, since
(x + a) - b = x + (a - b)
• a shift b units to the right and a units upward, since
(x + a) - b = x + (a - b) = x + (- b + a) = (x - b) + a.