Example 1

The function \(y = f(x)\) has a \(y\)-value of \(1\) at \((0, 1)\), so the graph of \(y = \frac{1}{f(x)}\) also passes through the point \((0, 1)\). Reciprocal functions of the form \(y = \frac{1}{f(x)}\) always have a horizontal asymptote at \(y = 0\). The graph of \(y = f(x)\) does not have any \(x\)-intercepts, so there are no vertical asymptotes on the graph of \(y = \frac{1}{f(x)}\).