Question

Estimate the average rate of change from x = 3 to x = 7.

Answer 1

To obtain the average rate of change from x = 3 to x = 7

We will have to obtain the corresponding values of y at the points x=3 and x=7

From the graph, we can observe that when x = 3, y = 1

also, when x = 7, y = 3

So the rate of change can be obtained by the formula:

=> change in y values/ change in x values

$\frac{y_2-y_1}{x_2-x_1}$

so let x1 =3, then y1 = 1

when x2= 7, y2 = 3

Upon substituting these values in the above equation

$\begin{gathered} \frac{3\text{ -1}}{7\text{ -3}} \\ =\frac{2}{4} \\ =\text{ 0.5} \end{gathered}$

rate of change = 0.5