Graphing reciprocals of quadratic functions

Graphing reciprocals of quadratic functions

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.

Lessons

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!
  • 1.
    Given that f(x)=x29f(x)=x^2-9 , graph the reciprocal of the function f(x)f(x)

  • 2.
    Given that g(x)=2x2+2x+1g(x)=2x^2+2x+1, graph the reciprocal of the function g(x)g(x)

  • 3.
    Given that y=2x2+x+1y=-2x^2+x+1 , graph the reciprocal of yy

  • 4.
    Given that f(x)=x2+2x4f(x)=-x^2+2x-4 , graph the reciprocal of the function f(x)f(x)