Question

using the following table of function values, calculate the average rate of change on the interval -19, -14.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-19\) and \(b = - 14\), \(f(a)=77\), \(f(b)=-41\).

Step2: Substitute the values into the formula

Substitute \(a=-19\), \(b=-14\), \(f(a) = 77\), \(f(b)=-41\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-41-77}{-14-(-19)}\).
First, calculate the numerator: \(-41 - 77=-118\).
Second, calculate the denominator: \(-14+19 = 5\).
So the average rate of change is \(\frac{-118}{5}=-23.6\).

Answer:

\(-23.6\)