Question

find the average rate of change of $g(x)=-3x - 2$ between the points $(-1,1)$ and $(1,-5)$

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = g(x)\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Identify the values of \(x_1,y_1,x_2,y_2\)

Here, \(x_1=-1,y_1 = 1,x_2 = 1,y_2=-5\).

Step3: Substitute into the formula

Substitute the values into \(\frac{y_2 - y_1}{x_2 - x_1}\), we get \(\frac{-5 - 1}{1-(-1)}\).
First, calculate the numerator: \(-5 - 1=-6\).
Then, calculate the denominator: \(1-(-1)=1 + 1=2\).
So, \(\frac{-6}{2}=-3\).

Answer:

\(-3\)