Question

Algebra 2 HELP!!! PLEASE!
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

@Miracrown

Answer 2

@misty1212

Answer 3

@misty1212 i graphed it on geogebra and it shows that alexis is wrong

Answer 4

@jim_thompson5910 do you understand the question

Answer 5

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

Now can you figure out how one student talking about the endpoints and the other talking about the behavior in the middle can both be right?

Answer 6

so it's dependent upon the y values?

Answer 7

If y = 1 then the values between -1 and 1 will average out to be 0. It is also a function because it passes the vertical line test which says that every vertical line will pass through y = 1 once and only once. I'm not sure you can confine a function between 2 defined points. This is more like a line segment. However we will assume a segment can be a function. In addition this function has a rate of change of zero because it is zero anywhere between 1 and - 1 for x.

Alexis can be correct if you consider y = x^2. The same argument applies.

Hope that helps!

Answer 8

misty1212's graph shows how they are both correct

the average rate of change is equal to the slope, so if "average rate of change is 0", then slope = 0...ie we have a flat line

Answer 9

and i'm sure you can see the turning point as well