# 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
$y=0$
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) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!
• Introduction
Graph $f(x)= \frac{1}{x}$

• 1.
Given that $f(x)=4x$, graph the reciprocal of function $f(x)$

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

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

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

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