The average rate of change of a function f in an interval (a,b) is given by:
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
From the graph on function f we notice that f(-3)=-5 and f(-2)=-10, then forf we have:
[tex]\begin{gathered} m_f=\frac{f(-2)-f(-3)}{-2-(-3)} \\ m_f=\frac{-10-(-5)}{3-2} \\ m_f=\frac{-10+5}{1} \\ m_f=-5 \end{gathered}[/tex]
Fro the table defining dfunction g we have that g(-3)=19 and g(-2)=12, then we have:
[tex]\begin{gathered} m_g=\frac{g(-2)-g(-3)}{-2-(-3)} \\ m_g=\frac{12-19}{1} \\ m_g=-7 \end{gathered}[/tex]
Finally, for function h we have:
[tex]\begin{gathered} m_h=\frac{g(-2)-g(-3)}{-2-(-3)} \\ m_h=\frac{\lbrack-(-2)^2+(-2)+2\rbrack-\lbrack-(-3)^2+(-3)+2\rbrack}{-2-(-3)} \\ m_h=\frac{(-4-2+2)-(-9-3+2)}{1} \\ m_h=\frac{(-4)-(-10)}{1} \\ m_h=\frac{-4+10}{1} \\ m_h=6 \end{gathered}[/tex]
Now, that we have all the average rate of change we notice that:
[tex]m_g
Therefore, the order we have is g(x), f(x), h(x)
