Question

The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval −6≤x≤−2?

Answer 1

Note: Formula for average rate on {a, b}

`Average\text{ }Rate=(f(b)-f(a))/(b-a)`

From the question, we have

`\begin{gathered} a=-6 \\ b=-2 \\ f(a)=f(-6)=-2 \\ f(b)=f(-2)=-10 \end{gathered}`

Substituting the parameters

`\begin{gathered} Average\text{ }Rate(A.R)=(f(b)-f(a))/(b-a) \\ \\ A.R=(-10-(-2))/(-2-(-6)) \\ \\ A.R=(-10+2)/(-2+6) \\ \\ A.R=(-8)/(4) \\ \\ A.R=-2 \end{gathered}`

Average Rate of change = -2