For which interval is the function constant? (4, ∞) (0, 4) (−4, 0) (−∞, −4)

The interval from x = -4 to x = 0 is when the graph is completely flat. 

We can write this interval as -4 < x < 0 which becomes (-4,0) in interval notation

That's why the answer is choice C

Note: be careful not to mix up interval notation and ordered pair notation