Topic: Curve Analysis and Sketching

Rational End Behavior and Asymptotes

Polynomial End Behavior from Leading Terms

Parameter Changes in Families of Curves

Multiplicity and Polynomial Graph Crossing

Matching Roots, Turning Points, and Multiplicity

Local Shape Near Vertical Asymptotes

Limits as Local Graph Constraints

Intercepts and Symmetry in Curve Sketches

Inflection Points and Concavity Changes

Impossible Curve Sketches and Derivative Contradictions