Graphing reciprocals of linear functions

Graphing reciprocals of linear functions

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.

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) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!
  • Introduction
    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)

  • 2.
    Given that f(x)=x+5f(x)=x+5 , graph the reciprocal of function f(x)f(x)

  • 3.
    Given that f(x)=2x1f(x)=2x-1, graph the reciprocal of the function f(x)f(x)

  • 4.
    Given that y=125xy= \frac{1}{2}-5x , graph the reciprocal of yy

  • 5.
    Given that y=13x9y=\frac{1}{3}-\frac{x}{9} , graph the reciprocal of yy