Based on the graphs of functions f(x) and g(x) = f(x) + k, the value of k is 4.
In Mathematics and Euclidean Geometry, the translation a geometric figure upward means adding a digit to the value on the positive y-axis of the pre-image;
g(x) = f(x) + k
Conversely, the translation of a graph downward means a digit would be subtracted from the numerical value on the y-axis of the pre-image:
g(x) = f(x) - k
In this context, we can logically deduce that the graph of the function f(x) would shift k units up if the function were changed to g(x);
k = 2 - (-2)
k = 2 + 2
k = 4 (4 units up)