\({1\over f(x)}\)

The graph of f and \({1 \over f}\) intersect where \(f(x)=\pm 1\)

x intercepts of the function f become vertical intercepts of \({1 \over f}\)

Local maxima of f become local minima of \({1 \over f}\)

Local minima of f become local maxima of \({1 \over f}\)