Chapter ISG, Problem 3.3.10P

To determine

To calculate the rate of change in the given graph,

Answer to Problem 3.3.10P

Rate of change in the interval $x=-2$ to $x=4$ is,

0.5

Rate of change in the interval $x=0$ to $x=6$ is,

0.5

Explanation of Solution

Given information:

The intervals are,

  $x=-2$ to $x=4$

And $x=0$ to $x=6$

Formula used:

  $RateOfChange=\frac{y2-y1}{x2-x1}$

Calculation:

For $x=-2$ to $x=4$

Concluding from graph, value for y when $x=-2$ ,

  $y=-3$

Concluding from graph, value for y when $x=4$ ,

  $y=0$

For the rate of change, substituting the value,

  $RateOfChange=\frac{0-(-3)}{4-(-2)}$

So,

  $RateOfChange=\frac{3}{6}$

On solving,

  $RateOfChange=0.5$

Hence, rate of change in the interval $x=-2$ to $x=4$

is,

0.5

For $x=0$ to $x=6$

Concluding from graph, value for y when $x=0$ ,

  $y=-2$

Concluding from graph, value for y when $x=6$ ,

  $y=1$

For the rate of change, substituting the value,

  $RateOfChange=\frac{1-(-2)}{6-0}$

So,

  $RateOfChange=\frac{3}{6}$

On solving,

  $RateOfChange=0.5$

Hence, rate of change in the interval $x=0$ to $x=6$ is,

0.5