Question

the average rate of change from ( x = - 2 ) to ( x = 6 ) for the function shown in the graph is

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-2\), \(f(a) = 7\), \(b = 6\), and \(f(b)=3\).

Step2: Substitute the values into the formula

Substitute \(a=-2\), \(f(a) = 7\), \(b = 6\), and \(f(b)=3\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{3 - 7}{6-(-2)}=\frac{-4}{8}\).

Step3: Simplify the fraction

Simplify \(\frac{-4}{8}\) to \(-0.5\).

Answer:

\(-0.5\)