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Continuity and End Behavior of Polynomials

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….

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Continuity and End Behavior of Polynomials

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  1. Continuity and End Behavior of Polynomials

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

  3. Continuity… • Polynomial Functions - Continuous • Rational Functions – Discontinuity at…

  4. Continuity… • Other continuous functions: • Other functions with discontinuities:

  5. Continuity… Piece-wise Functions

  6. 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

  7. End Behavior… Four Prototypes: • Up on both ends… y = x2 • Down on both ends… y = -x2 • Up on the right & Down on the left… y = x3 • Up on the left & Down on the right… y = -x3

  8. Describe the End Behavior:

  9. 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…

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