In general, if you have a parent function, f(x), the graph of a daughter function f(x - h) + k is related with the graph of the parent function as per these rules:
- The constant h subtracted from the argument, x, translates the graph of the parent function, f(x), h units to the right.
- The constant k added to the function, f(x), translates the graph of the parent function, f(x), k units upward.
Therefore, the graph of f(x) = |x - h| + k is a translaion of h units to the right and k units upward fo the function f(x) = |x|.
Since, the graph of f(x) = |x| has vertex (0,0), the graph of f(x) = |x - h| + k has vertex (h, k).
To visualize the images of the graph, assume some positive value for h and k. For instance, h = 3 and k = 5.
See the image attached showing the graphs for the functions f(x) = |x| (red line) and f(x - 3) + 5 = |x - 3| + 5 (blue line). As you can see, the blue line is the translation of the red line 3 units to the right and 5 units upward.