We can answer the question by just looking at the horizontal line. The horizontal line goes through y = 5 where the values in the x-axis are between 1 and 4 without including them.
So, the only piecewise function that has one of the equations as:
f(x) = 4 for 1 < x < 4
is the option A.
We can also prove that for x less than 1, the equation of the line is f(x) = x+ 1 and for x greater or equal to 4, the equation of the line is f(x) = x - 1
For example: the first line goes through the point (0,1), so if x is equal to 0 (less than 1),
f(x) = x + 1 = 0 + 1 = 1
So, the answer is A
