# Graphing reciprocals of linear functions

0/1

### Introduction

#### Lessons

1. Graph $f(x)= \frac{1}{x}$
0/5

### Examples

#### Lessons

1. Given that $f(x)=4x$, graph the reciprocal of function $f(x)$
1. Given that $f(x)=x+5$ , graph the reciprocal of function $f(x)$
1. Given that $f(x)=2x-1$, graph the reciprocal of the function $f(x)$
1. Given that $y= \frac{1}{2}-5x$ , graph the reciprocal of $y$
1. Given that $y=\frac{1}{3}-\frac{x}{9}$ , graph the reciprocal of $y$

## Become a Member to Get More!

• #### Easily See Your Progress We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.

• #### Make Use of Our Learning Aids   ###### Practice Accuracy

See how well your practice sessions are going over time.

Stay on track with our daily recommendations.

• #### Earn Achievements as You Learn   Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.

• #### Create and Customize Your Avatar   Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Basics
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
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!