Question

find the average rate of change of ( g(x) = 3x - 6 ) from ( x = -2 ) to ( x = 2 ). simplify your answer as much as possible.

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( g(x) \) from \( x = a \) to \( x = b \) is given by \( \frac{g(b)-g(a)}{b - a} \). Here, \( a=-2 \), \( b = 2 \), and \( g(x)=3x - 6 \).

Step2: Calculate \( g(-2) \)

Substitute \( x=-2 \) into \( g(x) \):
\( g(-2)=3(-2)-6=-6 - 6=-12 \)

Step3: Calculate \( g(2) \)

Substitute \( x = 2 \) into \( g(x) \):
\( g(2)=3(2)-6=6 - 6 = 0 \)

Step4: Apply the average rate of change formula

Using the formula \( \frac{g(b)-g(a)}{b - a} \), substitute \( a=-2 \), \( b = 2 \), \( g(-2)=-12 \), and \( g(2)=0 \):
\( \frac{g(2)-g(-2)}{2-(-2)}=\frac{0-(-12)}{2 + 2}=\frac{12}{4}=3 \)

Answer:

\( 3 \)