Question

Explain why the graphs of f(x) =x and g(x) =1/x are in the same quadrants over the same intervals. Does this relationship hold for m(x) = -x and n(x) = -1/x? Does this relationship hold for any function and its reciprocal function.

Answer 1

if x is positive, so is 1/x.
If x is negative, so is 1/x

So, the graphs lie in QI and QIII

apply that logic to m(x) and n(x)