Question

What is the average rate of change for this quadratic function for the intervalfrom x= -5 to x = -3?A. 8B. -16C. -8D. 16

Answer 1

We have to calculate the average rate of change foro this quadratic function in the interval x =-5 to x = -3.

The average rate of change for a function f(x) in the interval [a,b] can be calculated as:

`r=(f(b)-f(a))/(b-a)`

We then need to now f(-5) and f(-3).

We can identify this values in the graph as:

We can then calculate the average rate of change as:

`\begin{gathered} r=(f(-5)-f(-3))/(-5-(-3)) \\ r=(-15-1)/(-5+3) \\ r=(-16)/(-2) \\ r=8 \end{gathered}`

Answer: the average rate of change in this interval is 8 [Option A]