Question

Which function has an average rate of change of -4 over the interval (-2, 2];A.-2-112olopir)125-3-4B.-2-1012mir)-12-5-4-34Ос.-2--1012gir)-400-4-12D.r-2-1012nir)-60006

Answer 1

The average rate of change is given by:

$r=\frac{f(b)-f(a)}{b-a}$

For p(x):

$r=\frac{p(2)-p(-2)}{2-(-2)}=\frac{-4-12}{2+2}=\frac{-16}{4}=-4$

For m(x):

$r=\frac{m(2)-m(-2)}{2-(-2)}=\frac{4-(-12)}{2+2}=\frac{16}{4}=4$

For q(x):

$r=\frac{q(2)-q(-2)}{2-(-2)}=\frac{-12-(-4)}{2+2}=\frac{-8}{4}=-2$

For n(x):

$r=\frac{n(2)-n(-2)}{2-(-2)}=\frac{6-(-6)}{2+2}=\frac{12}{2}=6$

Therefore, the function which has an average rate of change of -4 over the interval [-2,2] is p(x).