Question

what is the average rate of change of f(x), represented by the graph , over the interval [-1,2]

Answer 1

C

Step-by-step explanation:

Formula for average rate of change :

[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]

Here :

b = 2

a = -1

f(b) = 2.5 (according to the graph)

f(a) = -5 (according to the graph)

Solving :

A(x) = 2.5 - (-5) / 2 - (-1)

A(x) = 7.5/3

A(x) = 2.5

Answer 2

C

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ - 1, 2 ] , then

f(b) = f(2) = 2.5 ← value of y from graph

f(a) = f(- 1) = - 5 ← value of y from graph , then

average rate of change = [tex]\frac{2.5-(-5)}{2-(-1)}[/tex] = [tex]\frac{2.5+5}{2+1}[/tex] = [tex]\frac{7.5}{3}[/tex] = 2.5