The absolute value of x means that all negative values are transformed into positive values.
Graphing the absolute value function, we have:
Then, in order to graph the function g(x) = |x + 7|, let's first calculate some points that are solutions to this equation:

Graphing g(x), we have:
The transformation needed to graph g(x) from f(x) is a translation (horizontal shift) of 7 units left.
Therefore the correct option is D.