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Graphing reciprocals of quadratic functions

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  1. Given that f(x)=x2−9f(x)=x^2-9 , graph the reciprocal of the function f(x)f(x)
    1. Given that g(x)=2x2+2x+1g(x)=2x^2+2x+1, graph the reciprocal of the function g(x)g(x)
      1. Given that y=−2x2+x+1y=-2x^2+x+1 , graph the reciprocal of yy
        1. Given that f(x)=−x2+2x−4f(x)=-x^2+2x-4 , graph the reciprocal of the function f(x)f(x)
          Topic Notes
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          We have learnt the basics of reciprocal functions. In this section, we will learn how to graph the reciprocal of a quadratic function, while applying the same principles we used when graphing the reciprocal of a linear function, while following the "6-steps Approach" noted below.
          Steps to graph the reciprocal of a function:
          1) Plot a horizontal asymptote
          at
          y=0y=0
          2) Plot vertical asymptote(s)
          equate the original function to 0; solve for xx
          3) Plot y-intercept(s)
          1y-intercept(s) of the original function\frac{1}{\text {y-intercept(s) of the original function}}
          4) Plot invariant points:
          equate the original function to +1 and -1; solve for xx
          5) Plot
          1vertex of the original function\frac{1}{\text {vertex of the original function}}
          6) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!