what is the average rate of change of f(x) from x1 = -9 to x2 = -2? please write your answer as an integer…
what is the average rate of change of f(x) from x1 = -9 to x2 = -2? please write your answer as an integer or simplified fraction. f(x) = 6x + 3
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ from $x_1$ to $x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.
Step2: Calculate $f(x_1)$
Given $f(x)=6x + 3$ and $x_1=-9$, then $f(x_1)=6\times(-9)+3=-54 + 3=-51$.
Step3: Calculate $f(x_2)$
Given $x_2=-2$, then $f(x_2)=6\times(-2)+3=-12 + 3=-9$.
Step4: Substitute into formula
$\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{-9-(-51)}{-2-(-9)}=\frac{-9 + 51}{-2 + 9}=\frac{42}{7}=6$.
Answer:
$6$