Unit G Summary Question #7: Vertical Asymptote Limit Notation

#7: Describe how to write the limit notation for vertical asymptotes and what the notation means.

Once you have found the vertical asymptote(s) [go back to Unit G Summary Question #4], you include those values in your limit notation. Make sure to graph the equation on your graphing calculator and because you will be using it to find the notation.

PLEASE NOTE: - sign on the right of the number means it is to the left of the vertical asymptote [ex. 2-] it does NOT mean its a negative, if it were if would look like -2 -. A + sign on the right of the number means it is on the right of the vertical asymptote. [ex. 2+] Also, recall that a + ∞ symbol means that the graph is going upwards and that a - ∞ symbol means that the graph is going downwards.

Lets use this picture as an example. As you can see, the vertical asymptotes are located where x=-1 and where x=1. Now you look the the left of the -1 vertical asymptote line and you see that the graph is going upwards. This is notated as follows: as x--> -1-, f(x)--> +∞. Next look at how to the right of the 
-1 vertical asymptote line the graph goes down and so it is notated as : as x--> -1+, f(x)--> -∞. Let's move onto the asymptote line of x=1. To the left of this line the graph is going down and so it is written as: as x--> 1-, f(x)--> -∞. Finally, we look to the right of this line and we see that the graph goes upwards there fore it is written as : as x--> 1+, f(x)--> +∞