Question

based on the graphs of f(x) and g(x) below, answer the following questions.

Answer 1

To solve this question we will use the following formula for the average rate of change of a function h(x) over the interval a$\Delta_{a,b}h=\frac{h(b)-h(a)}{b-a}\text{.}$a) From the given graph we get that f(2.2)=2.9, and f(6.1)=4.9, therefore:

$\begin{gathered} \Delta_{2.2,\text{ 6.1}}f=\frac{f(6.1)-f(2.2)}{6.1-2.2}=\frac{4.9-2.9}{6.1-2.2} \\ =\frac{2}{3.9}=\frac{20}{39}. \end{gathered}$

b) From the given graph we get that g(2.2)=2.9, and g(6.1)=4.9, therefore:

$\begin{gathered} \Delta_{2.2,\text{ 6.1}}g=\frac{g(6.1)-g(2.2)}{6.1-2.2}=\frac{4.9-2.9}{6.1-2.2} \\ =\frac{2}{3.9}=\frac{20}{39}. \end{gathered}$

Answer:

a)

$\frac{20}{39}\text{.}$

b)

$\frac{20}{39}\text{.}$