Curve Sketching

Tuesday, 17 April 2018

9:44 PM

Cartesian Equations Checklist

• Domain of the equation
•  and  intercepts
• Symmetry & Period
• Limits
• Asymptotes
• Stationary points
• Sections of increase and decrease

 

Asymptotes

Definition: A straight line which is approached closer and closer to (but never reached) by the curve

Vertical Asymptotes

Condition: Zero exists in the denominator

Form:

Definition:  as  or

 

Horizontal Asymptotes

Condition:

Form:

Definition:

 

Oblique Asymptote

Condition:  or  or the numerator is of one degree higher than the denominator

Form:

Definition:

Definition:  with

 

Such that

 

Symmetry

 is even if

 is odd if

 

Periodicity

 is periodic of  if