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.