What is the average rate of change between x = -1 and x = 1?

Question

Answers

a.- 4

b.-3

c.-1/3

b. undefined

Answer 1

If a function, f(x), is continuous (that is, has values for every x in the interval) from x=- 1 to x=1 ), then the average rate of change is:

( total amount that f(x) changes ) / (total amount that x changes)

( f(1) - f(-1) ) / ( (1) - (-1) )

( f(1) - f(-1) ) / 2

The variable x changes from (-1) to (1). That value is 2. [note: (1)-(-1) ]

The function changes from f(-1) to f(1). You must determine f(1)-f(-1) and use that value as the numerator.

Fill in the values to determine the average rate of change: ( f(1) - f(-1) ) / 2

However, if the plot of y values is not a function, and there is some x value between -1 and 1 for which f(x) is undefined, then the rate of change of y from f(-1) to f(1) is also undefined.