Even if there is some variation, the average rate

of change over an interval is zero if y(x) has

the same value at the beginning and end of the



Let's look at the interval −6 < x < −2.


y(−6) = −3


y(−2) = 2


y(x) goes up by 5 over this interval, so the

rate of change isn't zero.




How can you jump to the literal value of an



y(-6) = -3 (Good to go)


y(−2) = 2 (No so good to go)


First of all, based on the given graph values of y as

x is approaching -2 from the negative, are all y = -3.

The interval choice of −6 < x < −2 clearly originates

(-6) and terminates (< −2) which is anything less than -2,

and therefore defined, where y is exclusively in the -3

range, for the given domain.


The only way that y(-2) = 2, would be if the range

would be defined as:


−6 < x [≤] −2, and not −6 < x [<] −2.