Question

The functions f(x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 2−2≤x≤2 goes from least to greatest.

Answer 1

The formula for the average rate of change of a function is;

`m=(y_2-y_1)/(x_2-x_1)`

For f(x);

`\begin{gathered} m=(30-(-10))/(2-(-2)) \\ m=10 \end{gathered}`

For (x):

`\begin{gathered} m=(10-46)/(2-(-2))= \\ m=-9 \end{gathered}`

For h(x):

`\begin{gathered} m=(h(2)-h(-2))/(2-(-2)) \\ m=((-2^2-5(2)+25)-(-(-2)^2-5(-2)+25))/(2-(-2)) \\ m=-5 \end{gathered}`

From this calculation, ranking the average rateof change from least to greatest, swe have;

`g(x),h(x),f(x)`