Question

1. information about a function g(x) is given in the table. the function g(x) is defined for all real numbers.

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$$\begin{array}{|c|c|c|c|c|c|c|} \\hline x& - 5&-5 < x < - 2&-2&-2 < x < 4&4&4 < x < 7&7\\ \\hline g(x)&8&increasing&11&decreasing&2&decreasing&-4\\ \\hline \\end{array}$$

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find the average rate of change of g(x) on the interval -2,4.

Explanation:

Step1: Recall the average - rate - of - change formula

The formula for the average rate of change of a function $y = g(x)$ on the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-2$ and $b = 4$.

Step2: Identify $g(a)$ and $g(b)$ from the table

From the table, when $x=-2$, $g(-2)=11$, and when $x = 4$, $g(4)=2$.

Step3: Calculate the average rate of change

Substitute $a=-2$, $b = 4$, $g(-2)=11$, and $g(4)=2$ into the formula: $\frac{g(4)-g(-2)}{4-(-2)}=\frac{2 - 11}{4 + 2}=\frac{-9}{6}=-\frac{3}{2}$.

Answer:

$-\frac{3}{2}$