Question

Find the average rate of change of the function f(x), represented by the graph, over the interval [-4, -1]. Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula . The value of f(-1) is . The value of f(-4) is . The average rate of change of f(x) over the interval [-4, -1] is .

Answer 1

if we take a peek at the graph, the y-coordinate at x = -4 is y = -3, and the y-coordinate at x = -1, is y = 3,

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} x_1=-4\\ x_2=-1 \end{cases}\implies \cfrac{f(-4)-f(-1)}{-4-(-1)}\implies \cfrac{-3~~-~~(3)}{-4-(-1)}\implies \cfrac{-6}{-4+1} \\\\\\ \cfrac{-6}{-3}\implies 2$

Answer 2

Answer:

f(-4)= -3

f(-1)= 3

Rate of change= 2

Step-by-step explanation:

We are asked to find the rate of change of f(x) over the interval:

[-4,-1]

We know that a rate of change of a function f(x) over the interval [a,b] is given by:

$Rate\ of\ change=\dfrac{f(b)-f(a)}{b-a}$

Here we have:

a= -4 and b= -1

Clearly from the graph we have:

The value of f(-1) is 3.

The value of f(-4) is -3.

The average rate of change of f(x) over the interval [-4, -1] is calculated by:

$=\dfrac{3-(-3)}{-1-(-4)}\\\\\\=\dfrac{3+3}{-1+4}\\\\=\dfrac{6}{3}\\\\=2$

Hence, Rate of change over the interval [-4,-1] is: 2