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