Which values should I use to graph the rational function y = 1/x-2 - 6? (The asymptotes are x = 2; y = -6.)

Question

Also, what method could I use to choose values for graphing rational functions?

Answer 1

first, draw the asymptotes. Then pick a few values of x near the vertical asymptotes, so you get a feel for how y behaves in that region.

Then pick a few more values a little farther away, and draw the curve, keeping in mind that it will approach the horizontal asymptote on the sides.

And watch out -- sometimes the graph will cross the horizontal asymptote and approach it from the other side. As with something like x/(x^2+1):

http://www.wolframalpha.com/input/?i=x%2F%28x^2%2B1%29

Answer 2

3(x+2)=3x+6