Simple Rational Functions - Asymptotes
A simple rational function is any functionof the formwhereandare constants.
We can perform long division on this to obtain
This is a transformation of the graphThe transformation is in three steps:
A translation to the left, the negative– direction, by
A scaling in the- direction byIf this expression is negative, then the graph is reflected in the– axis and scaled.
A translation in the– direction by
The asymptotes are also transformed. The– asymptotebecomes the– asymptoteTheasymptotebecomes the– asymptote
Suppose for example that
Proceeding as above,
1. A translation to the left, the negative– direction, by
A reflection in the x – axis and scaling in the- direction by
A translation in the– direction byTheandasymptotes becomeandrespectively.
The transformation is shown below.