The average rate of change in a function is determined by :
[tex]=\frac{f(b)-f(a)}{b-a}[/tex]
Where :
a = lower limit
b = upper limit
f(a) = value of the function at the lower limit
f(b) = value of the function at the upper limit
From the given problem :
[tex]-7\leqslant x\leqslant6[/tex]
The lower limit is -7 and the upper limit is 6.
So we can say that a = -7 and b = 6
Looking at the figure when x = -7, f(x) = -10
when x = 6, f(x) = -5
Then we can also say that f(a) = -10
and f(b) = -5
Substitute the given values to the formula :
[tex]=\frac{-5-(-10)}{6-(-7)}[/tex][tex]=\frac{5}{13}[/tex]
Therefore, the average rate of change is :
[tex]\frac{5}{13}[/tex]
