Graph the y = function and identify the zeros (x-intercepts).
For the reciprocal function, 1/0 is undefined, so these are the locations of the vertical asymptotes.
Sketch the vertical asymptotes.
Mark the places where y = 1 or −1. These points do not change because 1/1 = 1 and 1/−1 = −1.
The reciprocal at the point (0, −4) is (0, −1/4). Mark it.
Draw a smooth curve from it to where y = −1 is marked and to where y = 1 is marked.
When the y-values of the original function are small, 1/(± small number) is a ± large number. Show this on your graph.
When the y-values of the original function are large, 1/large number is a small number. Show this on your graph.