Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = -3 and x = 3, the average rate of change is 0. Karly says that for the function, between x = -3 and x = 3, the graph goes up through a turning point, and then back down. Explain how Tucker and Karly can both be correct, using complete sentences.

Question

anonymous · Answer

someone please please help

anonymous · Answer

|dw:1419886341290:dw|

anonymous · Answer

average rate is zero since it is equal at each endpoint
but it goes up, and comes back down

anonymous · Answer

So that's why they are both correct?

anonymous · Answer

if you want a specific example you could say 
$$f(x)=4-x^2$$ on the interval $(-3,3)$ the average rate is zero because 
$$f(3)=f(-3)=-5$$ but the function goes up from $-5$ to  $4$ and back down to $-5$ so yes, they can both be correct

anonymous · Answer

here is a better picture as an example http://www.wolframalpha.com/input/?i=4-x^2+domain+-3..3

anonymous · Answer

here is an even better picture https://www.youtube.com/watch?v=UpsKGvPjAgw

anonymous · Answer

you just sent me a link to one directions song steal my girl?

anonymous · Answer

lol

anonymous · Answer

the first link is to the graph

anonymous · Answer

Haha okay thank you so much :) how do I like fan you or give you a medal for helping.. I literally just made my account a second ago.. don't know how to use the website yet..

anonymous · Answer

you can click "best response" for a medal, but i cannot cash them  in for valuable prizes and merchandise so it is ok either way
many people like them though
i am fine with  "thanks"

anonymous · Answer

and you are welcome