function

Function Delight

(Sung to the tune, "Silent Night")


Function Delight! Rationals in Sight!
Features Blaze, With Foresight
Forbidden Values Restrict the Domain
Listen Closely to Their Soft Refrain...
Asymptotes or Holes Live Here;
Some Special Feature Lives Here!

Silent Night, Holey Sight...
Rationals... Features Bright
Holes Contained at Forbidden Space
Reduced Functions Reveal the Place
I am Certain They're There!
Ratios of Zeros Declare!

Asymptotes, Vertical Kinds...
Forbidden x: Wrongly Assigned!
Non-Zero Values Divided by Nought
In the Original, Havoc is Wrought...
Infinite Values are Here
Vertical Asymptote, clear!

Asymptotes, Horizontal...
Changes in y's Become Real Small,
As x's get Infinite, Barriers Emerge
Limits then Force the Sweet Graph to Converge
Getting Close to Horizons,
Its Reaching Horizontal.

Asymptotes, Obliques Aglow...
Lower Degrees, Ratioed Below...
Long Divide and Discard the Remains
Quotients Provides us with Excellent Gains
Rationals Tend Toward these Guys...
With x's of Infinite Size.