Given that $f(x)=x^2-9$ , graph the reciprocal of the function $f(x)$

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

Given that $y=-2x^2+x+1$ , graph the reciprocal of $y$

Given that $f(x)=-x^2+2x-4$ , graph the reciprocal of the function $f(x)$

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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 $y=0$
2) Plot vertical asymptote(s) equate the original function to 0; solve for $x$
3) Plot y-intercept(s) $\frac{1}{\text {y-intercept(s) of the original function}}$
4) Plot invariant points: equate the original function to +1 and -1; solve for $x$
5) Plot $\frac{1}{\text {vertex of the original function}}$
6) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!