1) Plot a horizontal asymptote at $y=0$

2) Plot vertical asymptote(s) equate the original function to 0; solve for $x$

3) Plot y-intercept(s) $\frac{1}{\text {y-intercept(s) of the original function}}$

4) Plot invariant points: equate the original function to +1 and -1; solve for $x$

5) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!