Question

John was graphing a function and noticed that at certain points, the graph reaches invisible lines the graph will never cross. Explain to John what the two types of invisible lines are and how to predict them. You may create your own example to aid in your reasoning. Use complete sentences.

Answer 1

          In fact there are 3 types of invisible lines that the graph reaches but will never cross. These lines are called asymptotes. 
          An asymptote of a graph is a line such that the distance between the line and the curve approaches zero as they tend to infinity.
          There are: vertical, horizontal and oblique asymptotes.
          For example: 
          f ( x ) = 1 / (x + 2)
          Vertical asymptote is : x = -2 because:
            lim   1 / ( x + 2 ) = 1/ 0 = ∞
           x→-2
         Horizontal asymptote is y = 0 because:
           lim   1 / ( x + 2 ) = 1 / ∞ = 0
          x→∞