Question

Determine the average rate of change over left curly bracket negative 4 less or equal than x less or equal than 4 bold right curly bracket. Do NOT simplify.

Answer 1

{-4≤ x≤ 4}

The average rate of change would be 1 for f(x) = x.

Explanation:

Suppose we have a range a≤x≤b, then the average rate of change can be calculated by =f(b) - f(a)/b-a

The given range lies from -4 to 4 as {-4≤ x≤ 4}

The range of this is from -4 to 4.It includes all the numbers ranging from -4 to 4.

The average rate of change of the function is calculated by

= f(4) - f(-4)/4-(-4)

Suppose f(x)= x then f(4)= 4 and f(-4)= -4

Then

4- (-4)/ 4- (-4)

= 8/8= 1

So the average rate of change would be 1.