Question

URGENT PLEASE HELP

Use the table below to answer this question:

x y
-1 5
1 3
4 0
Find the average rate of change for the given function from x = −1 to x = 4.

Answer 1

Average rate of change = slope = (5-3)/(-1-1)=2/-2=-1

Answer 2

Average rate of change (A(x)) for the function y=f(x) over interval [a, b] is given by:

`A(x) = (f(b)-f(a))/(b-a)`

As per the statement:

x y

-1 5

1 3

4 0

To find the average rate of change for the given function from x = −1 to x = 4.

At x = -1

⇒y = 5

and

At x = 4 ,

⇒y = 0

Substitute these values we have;

`A(x) = (f(4)-f(-1))/(4-(-1))=(f(4)-f(-1))/(5)`

⇒
`A(x) = (0-5)/(5) = (-5)/(5) = -1`

Therefore, the average rate of change for the given function from x = −1 to x = 4 is, -1