Question

Find the average rate of change of the function defined by the following table. x y -2 -5 2 35 6 75 10 115

Answer 1

By definition we have that the average rate of change of the function is:

 $AVR = \frac{f(x2) - f(x1)}{x2 - x1}$

 Evaluating the function for the complete interval we have that the AVR is given by:

 $AVR = \frac{115 - (-5)}{10 - (-2)}$

 Rewriting we have:

 $AVR = \frac{115+5}{10+2}$

 Simplifying the expression we have:

 $AVR = \frac{120}{12}$

 $AVR = 10$

 Answer:

 the average rate of change of the function defined by the table is:

 $AVR = 10$