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Continuity endbehavior
All polynomial functions are continuous, while rational functions can be discontinuous at points where the denominator is zero. The document discusses the continuity and end behavior of polynomials, noting there are four possibilities for their end behavior: up on both ends, down on both ends, up on the right and down on the left, or up on the left and down on the right. It provides examples of polynomial functions that demonstrate each type of end behavior.
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Continuity endbehavior
- 1. Continuity and End Behavior of Polynomials
- 2. Continuity... All polynomialfunctions are continuous. Discontinuities – Three types: Infinite (VA) Point (Hole) Jump
- 3. Continuity… Polynomial Functions- Continuous Rational Functions – Discontinuity at…
- 4. Continuity… Other continuousfunctions: Other functions with discontinuities:
- 5. Continuity… Piece-wiseFunctions
- 6. End Behavior… FourPossibilities 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… FourPrototypes: 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
- 8. Describe the EndBehavior:
- 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…
Editor's Notes
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- #3 Open your presentation with an attention-getting incident. Choose an incident your audience relates to. The incidence is the evidence that supports the action and proves the benefit. Beginning with a motivational incident prepares your audience for the action step that follows.
- #4 Next, state the action step. Make your action step specific, clear and brief. Be sure you can visualize your audience taking the action. If you can’t, they can’t either. Be confident when you state the action step, and you will be more likely to motivate the audience to action.
- #5 To complete the Dale Carnegie Training® Evidence – Action – Benefit formula, follow the action step with the benefits to the audience. Consider their interests, needs, and preferences. Support the benefits with evidence; i.e., statistics, demonstrations, testimonials, incidents, analogies, and exhibits and you will build credibility.
- #6 To complete the Dale Carnegie Training® Evidence – Action – Benefit formula, follow the action step with the benefits to the audience. Consider their interests, needs, and preferences. Support the benefits with evidence; i.e., statistics, demonstrations, testimonials, incidents, analogies, and exhibits and you will build credibility.
- #7 To close, restate the action step followed by the benefits. Speak with conviction and confidence, and you will sell your ideas.
- #8 To close, restate the action step followed by the benefits. Speak with conviction and confidence, and you will sell your ideas.
- #9 Next, state the action step. Make your action step specific, clear and brief. Be sure you can visualize your audience taking the action. If you can’t, they can’t either. Be confident when you state the action step, and you will be more likely to motivate the audience to action.
- #10 To close, restate the action step followed by the benefits. Speak with conviction and confidence, and you will sell your ideas.