I am a bit confused about vertical asympotes. These two examples show different ways of getting asympotes. If I was to follow the first example to get the second example's asympote, it would not work out. Which example is correct, or are they both?

Question

1. 2x/x^2-1 becomes factored to equal: 2x/(x-1)(x+1). So the asympotes are -1 for the first parenthesis and 1 for the second. The asympote was found by taking the number beside the x.

2. x/x^2-2x-3 factors to x/(x-3)(x+1) The asympotes according to the algebra book are three and -1. They were found not by taking the number beside the x as in the previous example, but by adding the number that would equal zero in the place of the x.

Which method is correct?

Thanks for your help -Gina

Answer 1

Those actually both use the same method, the one you described for the second example. x=(-1) makes (x+1) equal to zero, and x=1 makes (x-1) equal to zero.

Answer 2

Using the value of 0.9%, the population in Texas is 25,145,561. How long and in what year may double assuming a steady growth rate.Starting in year 2011 to 2020?