There are simple steps and rules to follow when Graphing Rational Functions.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
First, we need to make sure that our function is in it’s lowest terms. This means that we need to check for any Removable Discontinuity (holes).
Next, we locate all of our Vertical Asymptotes by setting our denominator equal to zero. Remember, we can never ever touch a Vertical Asymptote, so it’s very important that we find these x-values at the beginning of our problem so we know what we need to avoid.
Then, we look at the degrees of both the numerator and the denominator and find our Horizontal or Oblique Asymptotes.
Then we check for any y-intercepts, intercepts (zeros), or Points of Intersection (will our function cross or touch a Horizontal or Oblique Asymptote).
Rational Function with Removable Discontinuity
And lastly, we plot points and test our regions in order to create our graph!
Now some textbooks will have a different order or procedure for graphing Rational Functions than what you will see in this video, but what is important to note is that as long as we identify each and every essential element it doesn’t matter what order or steps you use…. I just find the ordered steps outlined above is the simplest and easiest to follow!
Moreover, it is also important to note that each and every graph that we will see in this lesson will have an interruption(s) or pieces, as Paul’s Online Notes calls them. These interruptions or pieces indicate values of discontinuity, but will also help us to identify symmetry and end behavior.
Together we are going to look at nine very classic questions where we will encounter all different types of Discontinuities (asymptotes and/or holes) and learn how to identify the Domain and Range and End Behavior.
Graphing Rational Functions – Video
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