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so f(x) - k, is simply appending a constant "k", and thus is a vertical shift by k units.
f(x+h) is changing whatever "x" was to "x+h", and therefore is shifting the function to the left by h units.
f(x-h), is about the same as before, but is doing a horizontal shift to the right by h units.
so f(x) - k, is simply appending a constant "k", and thus is a vertical shift by k units.
f(x+h) is changing whatever "x" was to "x+h", and therefore is shifting the function to the left by h units.
f(x-h), is about the same as before, but is doing a horizontal shift to the right by h units.