Continuity and End Behavior of Polynomials. Continuity... All polynomial functions are continuous. Discontinuities – Three types: Infinite(VA) Point(Hole)

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Presentation transcript:

Continuity and End Behavior of Polynomials

Continuity... All polynomial functions are continuous. Discontinuities – Three types: Infinite(VA) Point(Hole) Jump

Continuity… Polynomial Functions - Continuous Rational Functions – Discontinuity at…

Continuity… Other continuous functions: Other functions with discontinuities:

Continuity… Piece-wise Functions

End Behavior… Four Possibilities –Up on both ends –Down on both ends –Up on the right & Down on the left –Up on the left & Down on the right

End Behavior… Four Prototypes: –Up on both ends… y = x 2 –Down on both ends… y = -x 2 –Up on the right & Down on the left… y = x 3 –Up on the left & Down on the right… y = -x 3

Describe the End Behavior:

End Behavior… Notation: –Up on both ends… –Down on both ends… –Up on the right & Down on the left… –Up on the left & Down on the right…