From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Functions, Graphs, and Limits

Functions, Graphs, and Limits

At a Glance - How to Draw Rational Functions from Scratch

We now have enough tools to draw some complicated functions from scratch. Now we know how graphing calculators do it, and why they require the energy of four triple-A's.

When drawing a rational function f(x) from scratch, we need to know a lot of information, which can be nicely grouped into three big chunks.

  • We need to know where f has vertical asymptotes and/or holes.
  • We need to know the horizontal/slant/curvilinear asymptotes of f, if any.
  • We need to know about values of f. We found where f is undefined when we found the vertical asymptotes and holes; now we need to know where f(x) is 0, positive, and negative. We also want to know f(0), also called the y-intercept.

Example 1

Graph the function 


Example 2

Graph the function   .


Example 3

Graph the function  


Example 4

Graph the function

.

Label all asymptotes, intercepts, and holes.


Exercise 1

Graph the function. Label all asymptotes, intercepts, and holes.


Exercise 2

Graph the function. Label all asymptotes, intercepts, and holes. 


Exercise 3

Graph the function. Label all asymptotes, intercepts, and holes.


Exercise 4

Graph the function. Label all asymptotes, intercepts, and holes. 

  •  

Exercise 5

Graph the function. Label all asymptotes, intercepts, and holes.


People who Shmooped this also Shmooped...

Advertisement