The original function is
y = f(x)
The new function is
y = f(x - 4) + 1
This is a modulus function. It is a function that gives the absolute value of a number. Thus, We can write the original function as
y = IxI
Since the graph is pointing downwards, it means that it was reflected over the horizontal axis. Thus, the parent function is
y = - IxI
Recall, if a function, f(x) is shifted c units to the right, the new function would be f(x - c). Thus, y = Ix - 4I means that the function was shifted 4 units to the right.
Also, if a function, f(x) is shifted d units upwards, the new function would be f(x) + d. Thus,
y = Ix - 4I + 1 means that the function was shifted 1 unit upward. Thus, the graph of
y = f(x - 4) + 1 = Ix - 4I + 1 is shown below