find the average rate change as x moves from -9 to -6 for y=square root of -5-x

y = √(- 5 - x)

we can also write it as

f(x) = √(- 5 - x)

So

x1 = - 9 x2 = - 6

then

f(x1) = √(- 5 - x1) = √(- 5 - (- 9)) = √(- 5 + 9) = √4 = 2

f(x2) = √(- 5 - x2) = √(- 5 - (- 6)) = √(- 5 + 6) = √1 = 1

As the formula for average rate of change is

A(x) = f(x2) - f(x1) / x2 - x1

Then putting the values, we get

A(x) = 1 - 2 / - 6 - (- 9)

= 1 - 2 / - 6 + 9

= - 1 / 3

A(x) = - 1/3

Hence the average rate of change is - 1/3.

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