Question

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.

Answer 1

Average rate of change is computed from the endpoints. Average rate of change = 0 means the function has the same value at the end as it did in the beginning of the intervalm

Answer 2

If the average rate of change is zero, that means f(-1) = f(1). It does NOT mean that f(x) is the same for all -1 <= x <= 1.

Answer 3

ok

Answer 4

so alexis is wrong

Answer 5

In other words,

Well if we analyze the formula for average rate of change (y1-y2/x1-x2) then we know the change I'm y values must be zero, because we already know that the change in x values is 2. This means that if there is a turning point between x=-1 and x=1 then as long as the y values at these points are the same, then the average ROC is zero. For example if the y values are 2, 2-2 is zero, zero divided by 2 (change In x) is still zero.

Answer 6

yes she is

Answer 7

or at least i believe so

Answer 8

so what you put is the answer?

Answer 9

sorry i made a mistake

Answer 10

so alexis cant be correct

Answer 11

alexis is correct since the graph would go up from x=-1, then turn and come back down from x=1

Answer 12

so how can they both be correct

Answer 13

they can both be correct because the polynominal function can go through both points

Answer 14

so thats it for this question

Answer 15

yes.

Answer 16

thank you i have another question

Answer 17

okay

Answer 18

Your friend hands you a graph of the performance statistics of the latest powerboat to be produced. He says, “I know this graph is f(x) = –2(x – 4)3 – 3 but I can’t remember how it is related to the graph of x3.” Explain to your friend how the graph f(x) is a translation of the graph x3.

Answer 19

this question has been asked on openstudy before
http://inquus.org/updates/53a0a84ee4b0fb4d2b4a4c01

Answer 20

thanks

Answer 21

Your welcome!!