The graph y = -f(x) is the graph of y = f(x) reflected about the x-axis.
Here's why.
If for instance, y = 6 in y = f(x), y = -6 in y = -f(x). Upon graphing, the two values y = 6 and y = -6 are at the same distance from the x-axis, hence, reflected across the x-axis.