anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
Or, if x=0 is the vertex (of a parabola, for example)
anonymous
  • anonymous
ok, can you really quickly give me an example just so i can understand a little better

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SolomonZelman
  • SolomonZelman
|dw:1435798222113:dw|
anonymous
  • anonymous
how would that be written as a function?
SolomonZelman
  • SolomonZelman
Say, that is a parabola \(y=x^2\)
SolomonZelman
  • SolomonZelman
But that can be many functions... in fact infinite number of such functions.
SolomonZelman
  • SolomonZelman
I will give you a couple of classes of such functions.
SolomonZelman
  • SolomonZelman
i need to referesh the page, give me a sec
anonymous
  • anonymous
ok, thanks and take your time
SolomonZelman
  • SolomonZelman
ok
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle y=x^2+{\rm a} }\) 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)). ----------------------------------------------------
SolomonZelman
  • SolomonZelman
oh, my bad a little error
SolomonZelman
  • SolomonZelman
all these functions should ahev a- in front. \(\large\color{black}{ \displaystyle y=-x^{\rm w} }\) \(\large\color{black}{ \displaystyle y=-x^{\rm w}+{\rm a} }\) \(\large\color{black}{ \displaystyle y=-x^{\rm w}-{\rm a} }\)
SolomonZelman
  • SolomonZelman
|dw:1435799037236:dw|
SolomonZelman
  • SolomonZelman
are you lost?

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