Graphing reciprocals of linear functions

We know that taking the reciprocal of a very large number will grant us a very small number. Conversely, if we take the reciprocal of a very small number, we will obtain a very small number. What will happen if we take the reciprocal of a linear function? In this section, we will learn about the concept behind the reciprocal of a linear function, as well as how to graph it, while following the "5-steps Approach" noted below.

Steps to graph the reciprocal of a function:
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!