Unit 3 Rational Functions Our Main Goal To

Unit 3 Rational Functions

Our Main Goal: To pick out key features of Rational Functions; Use these key features to graph

Recall Polynomial Functions:

Here are some examples of Rational Functions …

And some more …

And even more …

Last one … This may seem intimidating but if we stick to the Key Features it’s really quite easy!

Key Features

Domain Note: The function is discontinuos (BREAKS) at these points → VERTICACL ASYMPTOTE or a HOLE (we’ll talk about these later) either a

Vertical Asymptote(s) NOTE: that if there is the same zero on the TOP AND THE BOTTOM we get a HOLE instead of a vertical asymptote. this is because we can cross of the common factors → more on this later!)

Behaviour at the Vertical Asymptote(s)

Behaviour at the Vertical Asymptote(s) Test 3. 000001 Test 2. 999999

Behaviour at the Vertical Asymptote(s)

End behavior

Behaviour at End Behaviours … Does it approach the horizontal asymptote from the top or the bottom? Enter a really BIG positive number and a really big negative number). The function CAN cross horizontal and oblique asymptotes. See the “summary chart” example for the final solution and graph.

See the “summary chart” example for the final solution and graph.