Answer:
-6
Step-by-step explanation:
The average rate of a function f(x) on the interval from x=a to x=b is [tex]\frac{f(b)-f(a)}{b-a}[/tex].
So in the problem you have from [tex]x=2[/tex] to [tex]x=4[/tex].
The average rate of the function from x=2 to x=4 is
[tex]\frac{f(4)-f(2)}{4-2}=\frac{f(4)-f(2)}{2}[/tex].
Now we need to find f(4) and f(2).
f(4) means what is the y-coordinate that corresponds to x=4 on the curve.
f(4)=-15 since the ordered pair at x=4 is (4,-15).
f(2) means what is the y-coordinate that corresponds to x=2 on the curve.
f(2)=-3 since the ordered pair at x=2 is (2,-3).
So let's plug in those values:
[tex]\frac{f(4)-f(2)}{4-2}=\frac{-15-(-3))}{2}[/tex].
Now we just simplify:
[tex]\frac{-15+3}{2}[/tex]
[tex]\frac{-12}{2}[/tex]
[tex]-6[/tex]
