Find the average rate of change of the function from $x _ { 1 } = 0 \text { to } x _ { 2 } = 3$ $$f ( x ) = - 4 x + 17$$
A) The average rate of change from $x _ { 1 } = 0$ to $x _ { 2 } = 3$ is 17 .
B) The average rate of change from $x _ { 1 } = 0$ to $x _ { 2 } = 3$ is 4 .
C) The average rate of change from $x _ { 1 } = 0$ to $x _ { 2 } = 3$ is $- 17$.
D) The average rate of change from $x _ { 1 } = 0$ to $x _ { 2 } = 3$ is $- 4$.
E) The average rate of change from $x _ { 1 } = 0$ to $x _ { 2 } = 3$ is 19 .

Question

Quizplus · Accepted Answer

The formula for the average rate of change of a function is: 
$$ \frac{f(x_2) - f(x_1)}{x_2 - x_1} $$
Plugging in the given values, we get: 
$$ \frac{f(3) - f(0)}{3 - 0} = \frac{(-4\cdot3 + 17) - (-4\cdot0 + 17)}{3-0} = -\frac{7}{3} = -2.33$$
Therefore, the average rate of change from $x_1 = 0$ to $x_2 = 3$ is approximately $-2.33$, which is closest to choice D, $-4$.

Find the Average Rate of Change of the Function From x