If we are given the function $f(x) = \frac{1}{x}$, we can change the horizontal asymptote by adding a constant to the function. For example, $g(x) = f(x) + 5$, makes the asymptote at $y = 5$.
How could we keep the point $(1, 1)$ on the function's curve, while still raising the asymptote. Of course, we should only be able to do this with $0 < c < 1$, where $c$ is the new vertical asymptote.