Oxford PAT 2012, Question 12


2 thoughts on “Oxford PAT 2012, Question 12

  1. Hi, may I know what is your thought process everytime you see this question?I go for long division, but that only gives me the vertical asymptote and i am pretty much stuck after that…

    1. There is a pretty standard way of sketching graphs for functions like this.

      1. Consider what happens when x tends to plus infinity and minus infinity. In this case, two of the terms tend to zero, and we are left with -1.
      2. Differentiate the expression if you can, and then differentiate it again to find maxima and minima (first differential is zero) and points of inflection (second differential is zero).
      3. Plug in any simple values of x that you can and find the corresponding y (e.g. try x = 0, +1, -1, etc).

      This should give you a bunch of points, so all you need to do now is join the dots. Remember that the curvature of the graph only changes when the second differential is zero.

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