Graphing reciprocals of linear functions

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  1. Graph f(x)=1x f(x)= \frac{1}{x}
  1. Given that f(x)=4xf(x)=4x, graph the reciprocal of function f(x)f(x)
    1. Given that f(x)=x+5f(x)=x+5 , graph the reciprocal of function f(x)f(x)
      1. Given that f(x)=2x1f(x)=2x-1, graph the reciprocal of the function f(x)f(x)
        1. Given that y=125xy= \frac{1}{2}-5x , graph the reciprocal of yy
          1. Given that y=13x9y=\frac{1}{3}-\frac{x}{9} , graph the reciprocal of yy
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            Topic Notes
            We know that taking the reciprocal of a very large number will grant us a very small number. Conversely, if we take the reciprocal of a very small number, we will obtain a very small number. What will happen if we take the reciprocal of a linear function? In this section, we will learn about the concept behind the reciprocal of a linear function, as well as how to graph it, while following the "5-steps Approach" noted below.
            Steps to graph the reciprocal of a function:
            1) Plot a horizontal asymptote
            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) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!