Solution:
The rate of change, m, of a function f is;
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
Given the graph, f(x);
Its rate of change over the given interval is;
[tex]\begin{gathered} m=\frac{f(4)-f(3)}{4-3} \\ \\ m=\frac{6-(-2)}{1} \\ \\ m=8 \end{gathered}[/tex]
Given the table of g(x);
Its rate of change over the interval is;
[tex]\begin{gathered} m=\frac{g(4)-g(3)}{4-3} \\ \\ m=\frac{13-18}{1} \\ \\ m=-5 \end{gathered}[/tex]
Also, given the function of h(x);
[tex]\begin{gathered} h(x)=-x^2+3x+21 \\ \\ h(4)=-(4)^2+3(4)+21 \\ \\ h(4)=-16+12+21 \\ \\ h(4)=17 \\ \\ h(3)=-(3)^2+3(3)+21 \\ \\ h(3)=-9+9+21 \\ \\ h(3)=21 \end{gathered}[/tex]
Its rate of change over the interval is;
[tex]\begin{gathered} m=\frac{17-21}{4-3} \\ \\ m=-\frac{4}{1} \\ \\ m=-4 \end{gathered}[/tex]
The order of the rate of change from the least to the greatest is;
[tex]-5,-4,8[/tex]
CORRECT OPTION:
[tex]g(x),h(x),f(x)[/tex]
