find average rate of change from equation score: 0/2 penalty: 0.5 off question given the function g(x)=x²…

find average rate of change from equation score: 0/2 penalty: 0.5 off question given the function g(x)=x² - 7x + 4, determine the average rate of change of the function over the interval 3 ≤ x ≤ 9. answer attempt 1 out of 2

Answer

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a = 3$, $b = 9$, and $g(x)=x^{2}-7x + 4$.

Step2: Calculate $g(9)$

Substitute $x = 9$ into $g(x)$: $g(9)=9^{2}-7\times9 + 4=81-63 + 4=22$.

Step3: Calculate $g(3)$

Substitute $x = 3$ into $g(x)$: $g(3)=3^{2}-7\times3 + 4=9-21 + 4=-8$.

Step4: Calculate the average rate of change

$\frac{g(9)-g(3)}{9 - 3}=\frac{22-(-8)}{6}=\frac{22 + 8}{6}=\frac{30}{6}=5$.