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.

We are given that the Wilson states that for the function f(x), -1≤x≤1 the average rate of change of the function is 0 i.e. .

Now, when we have , this implies that a function assume a critical point -1≤x≤1.

If a function has a critical point, we get that at that point the function either assumes its maximum or minimum value.

On the other hand, Alexis states that for the function f(x), -1≤x≤1 the graph goes up through a turning point and then goes back down.

This gives us that the function has a maximum value in -1≤x≤1 from where the graph changes its position from upward to downward.

So, we see that both Wilson and Alexis are implying that the function f(x) has a maximum value in -1≤x≤1.

Hence, both of them are correct in their statements.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is