Continuity    and  End Behavior    of Polynomials
Continuity... <ul><li>All polynomial functions are continuous. </li></ul><ul><li>Discontinuities – Three types: </li></ul>...
Continuity… <ul><li>Polynomial Functions - Continuous </li></ul><ul><li>Rational Functions – Discontinuity at… </li></ul>
Continuity… <ul><li>Other continuous functions: </li></ul><ul><li>Other functions with discontinuities: </li></ul>
Continuity…  Piece-wise Functions
End Behavior… <ul><li>Four Possibilities </li></ul><ul><ul><li>Up on both ends </li></ul></ul><ul><ul><li>Down on both end...
End Behavior… <ul><li>Four Prototypes: </li></ul><ul><ul><li>Up on both ends…  y = x 2 </li></ul></ul><ul><ul><li>Down on ...
Describe the End Behavior:
End Behavior… <ul><li>Notation: </li></ul><ul><ul><li>Up on both ends… </li></ul></ul><ul><ul><li>Down on both ends…  </li...
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Continuity endbehavior

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  • Selling your ideas is challenging. First, you must get your listeners to agree with you in principle. Then, you must move them to action. Use the Dale Carnegie Training® Evidence – Action – Benefit formula, and you will deliver a motivational, action-oriented presentation.
  • 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.
  • 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.
  • 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.
  • 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.
  • To close, restate the action step followed by the benefits. Speak with conviction and confidence, and you will sell your ideas.
  • To close, restate the action step followed by the benefits. Speak with conviction and confidence, and you will sell your ideas.
  • 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.
  • To close, restate the action step followed by the benefits. Speak with conviction and confidence, and you will sell your ideas.
  • Continuity endbehavior

    1. 1. Continuity and End Behavior of Polynomials
    2. 2. Continuity... <ul><li>All polynomial functions are continuous. </li></ul><ul><li>Discontinuities – Three types: </li></ul><ul><li>Infinite (VA) </li></ul><ul><li>Point (Hole) </li></ul><ul><li>Jump </li></ul>
    3. 3. Continuity… <ul><li>Polynomial Functions - Continuous </li></ul><ul><li>Rational Functions – Discontinuity at… </li></ul>
    4. 4. Continuity… <ul><li>Other continuous functions: </li></ul><ul><li>Other functions with discontinuities: </li></ul>
    5. 5. Continuity… Piece-wise Functions
    6. 6. End Behavior… <ul><li>Four Possibilities </li></ul><ul><ul><li>Up on both ends </li></ul></ul><ul><ul><li>Down on both ends </li></ul></ul><ul><ul><li>Up on the right & Down on the left </li></ul></ul><ul><ul><li>Up on the left & Down on the right </li></ul></ul>
    7. 7. End Behavior… <ul><li>Four Prototypes: </li></ul><ul><ul><li>Up on both ends… y = x 2 </li></ul></ul><ul><ul><li>Down on both ends… y = -x 2 </li></ul></ul><ul><ul><li>Up on the right & Down on the left… y = x 3 </li></ul></ul><ul><ul><li>Up on the left & Down on the right… y = -x 3 </li></ul></ul>
    8. 8. Describe the End Behavior:
    9. 9. End Behavior… <ul><li>Notation: </li></ul><ul><ul><li>Up on both ends… </li></ul></ul><ul><ul><li>Down on both ends… </li></ul></ul><ul><ul><li>Up on the right & Down on the left… </li></ul></ul><ul><ul><li>Up on the left & Down on the right… </li></ul></ul>

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