## 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.

1. 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.

2. SolomonZelman

Or, if x=0 is the vertex (of a parabola, for example)

3. anonymous

ok, can you really quickly give me an example just so i can understand a little better

4. SolomonZelman

|dw:1435798222113:dw|

5. anonymous

how would that be written as a function?

6. SolomonZelman

Say, that is a parabola $$y=x^2$$

7. SolomonZelman

But that can be many functions... in fact infinite number of such functions.

8. SolomonZelman

I will give you a couple of classes of such functions.

9. SolomonZelman

i need to referesh the page, give me a sec

10. anonymous

ok, thanks and take your time

11. SolomonZelman

ok

12. 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)). ----------------------------------------------------

13. SolomonZelman

oh, my bad a little error

14. SolomonZelman

all these functions should ahev a- in front. $$\large\color{black}{ \displaystyle y=-x^{\rm w} }$$ $$\large\color{black}{ \displaystyle y=-x^{\rm w}+{\rm a} }$$ $$\large\color{black}{ \displaystyle y=-x^{\rm w}-{\rm a} }$$

15. SolomonZelman

|dw:1435799037236:dw|

16. SolomonZelman

are you lost?