Question

Find the average rate of change on the interval [-2, 3] for each model. a. f(x)=√(x+6)

b. picture

Answer 1

The rate of change of a function f(x) on the interval [a, b] is found by
rate of change on [a, b] = (f(b) - f(a))/(b - a)

For your interval, that is
rate of change on [-2, 3] = (f(3) - f(-2))/(3 -(-2))
= (f(3) - f(2))/5

a. for the square root function, this is
rate of change = (f(3) - f(-2))/5 = (3 - 2)/5 = 1/5

b. for the graph, this is
rate of change = (f(3) - f(-2))/5 = (0 - (-5))/5 = 5/5 = 1