Question

Consider functions fg, and h below. 12 + 25 + 3 8 6 2 6 2 6 FB 2 6 8 Х 0 1 2. 3 h(x) -7 -4 -1 2 5

Answer 1

We have the functions,

$\begin{gathered} f(x)=x^2+2x+3 \\ \text{the rate of change of f(x) over (0,2 ) is } \\ rate-of-change=\frac{f(2)-f(0)}{2-0} \\ f(2)=2^2+2(2)+3=11 \\ f(0)=0^2+0+3=3 \\ so,\text{ average rate of change=}\frac{11-3}{2}=4 \end{gathered}$

We move over to g(x), g(x) is an exponential function;

$\begin{gathered} \text{From the graph,} \\ g(2)=7\text{ and g(0)=4} \\ so\text{ the average rate of change of g(x) over the interval (0,2) is} \\ \frac{g(2)-g(0)}{2-0} \\ =\frac{7-4}{2} \\ =\frac{3}{2}=1.5 \end{gathered}$

We move over to h(x),

$\begin{gathered} \text{From the table, h(0)=-4, h(2)=2} \\ \text{the rate of change of h(x) over the interval (0,2) is;} \\ \frac{2-(-4)}{2-0}=\frac{6}{2}=3 \end{gathered}$

If we rank the rates of change of the function , we see that,

$4>3>1.5$

So, the rates of change from least to greatest is;

g,h,f.

Option B