And we say that there are discontinuities in the function at the x-coordinates where it is undefined. Discontinuities are locations for x values that make the function undefined. Not all discontinuities in rational functions create vertical asymptotes, but these do. Some discontinuities are not asymptotic, but are removable. More about that later.
Vertical asymptotes show up as vertical white lines on the above applet.
Go ahead and try that . It should look like the following picture. To the immediate left of 6 the function outputs very large negative numbers making the graph of the function drop very steeply. Moving over by 0.001 usually works fine. Clearly, to the immediate left of the asymptote the function takes on an output value much more negative than can be seen on the above picture.