complete the sentence. for the function $f(x)=sqrt3{x - 2}$, the average rate of change to the nearest…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$, $b = 4$, and $f(x)=\sqrt[3]{x - 2}$.

Step2: Calculate $f(-2)$

Substitute $x=-2$ into $f(x)$: $f(-2)=\sqrt[3]{-2 - 2}=\sqrt[3]{-4}\approx - 1.59$.

Step3: Calculate $f(4)$

Substitute $x = 4$ into $f(x)$: $f(4)=\sqrt[3]{4 - 2}=\sqrt[3]{2}\approx1.26$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(4)-f(-2)}{4-(-2)}$, we substitute the values of $f(4)$ and $f(-2)$: $\frac{1.26-(-1.59)}{4 + 2}=\frac{1.26 + 1.59}{6}=\frac{2.85}{6}=0.48$.

Answer:

$0.48$