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anonymous

  • one year ago

PLEASE HELP ILL GIVE A MEDAL Two students in your class, Wilson and Alexis, are disputing a function. Wilson says that for the function, between x = -1 and x = 1, the average rate of change is 0. Alexis says that for the function, between x = -1 and x = 1, the graph goes up through a turning point, and then back down. Explain how Wilson and Alexis can both be correct, using complete sentences.

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  1. SolomonZelman
    • one year ago
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    The function they are disputing is not mentioned. They can be talking about different functions, and each one of them can be correct as regards to his own function.

  2. SolomonZelman
    • one year ago
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    Or, if x=0 is the vertex (of a parabola, for example)

  3. anonymous
    • one year ago
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    ok, can you really quickly give me an example just so i can understand a little better

  4. SolomonZelman
    • one year ago
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    |dw:1435798222113:dw|

  5. anonymous
    • one year ago
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    how would that be written as a function?

  6. SolomonZelman
    • one year ago
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    Say, that is a parabola \(y=x^2\)

  7. SolomonZelman
    • one year ago
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    But that can be many functions... in fact infinite number of such functions.

  8. SolomonZelman
    • one year ago
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    I will give you a couple of classes of such functions.

  9. SolomonZelman
    • one year ago
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    i need to referesh the page, give me a sec

  10. anonymous
    • one year ago
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    ok, thanks and take your time

  11. SolomonZelman
    • one year ago
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    ok

  12. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle y=x^2+{\rm a} }\) OR \(\large\color{black}{ \displaystyle y=x^2-{\rm a} }\) (where \(\rm a\) is any real number that is greater than zero) in fact, it can be any function: \(\large\color{black}{ \displaystyle y=x^{\rm w} }\) OR \(\large\color{black}{ \displaystyle y=x^{\rm w}+{\rm a} }\) OR \(\large\color{black}{ \displaystyle y=x^{\rm w} -{\rm a}}\) (where \(\rm w\) is some even, positive integer) ---------------------------------------------------- BUT absolute value is not (well, shouldn't be) an answer. Average rate of change between x=-1 and x=1 is 0, BUT (0,0) is a turning point ((recall the argument in the question)). ----------------------------------------------------

  13. SolomonZelman
    • one year ago
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    oh, my bad a little error

  14. SolomonZelman
    • one year ago
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    all these functions should ahev a- in front. \(\large\color{black}{ \displaystyle y=-x^{\rm w} }\) \(\large\color{black}{ \displaystyle y=-x^{\rm w}+{\rm a} }\) \(\large\color{black}{ \displaystyle y=-x^{\rm w}-{\rm a} }\)

  15. SolomonZelman
    • one year ago
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    |dw:1435799037236:dw|

  16. SolomonZelman
    • one year ago
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    are you lost?

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