Unit G Summary Question #4: Vertican asymptotes v. holes

4. What is the difference between a graph having a vertical asymptote and a graph having a hole?

The vertical asymptote and the hole fall into the same category because we factor the polynomials to find the vertical asymptotes and see if anything cancels. That is where the holes come in; they are the common factors in the numerator and denominator. They both go hand in hand because you have to make sure you use the simplified equation to find the vertical asymptotes, the domain, the x-intercept, and the y-intercept. However, the difference in finding the points is that for vertical asymptotes we are setting the simplfied bottom to 0 and that is our x= equation. For the holes, out "equation" is just a point (x,y) and we plug in the x value into the function and get the value.