Chapter ISG, Problem 3.3.9P

To determine

To calculate the rate of change in the given graph,

Answer to Problem 3.3.9P

Rate of change in the interval $x=-1$ to $x=3$ is,

-2

Rate of change in the interval $x=0$ to $x=4$ is,

-2

Explanation of Solution

Given information:

The intervals are,

  $x=-1$ to $x=3$

And $x=0$ to $x=4$

Formula used:

  $RateOfChange=\frac{y2-y1}{x2-x1}$

Calculation:

For $x=-1$ to $x=3$

Concluding from graph, value for y when $x=-1$ ,

  $y=5$

Concluding from graph, value for y when $x=3$ ,

  $y=-3$

For the rate of change, substituting the value,

  $RateOfChange=\frac{-3-5}{3-(-1)}$

So,

  $RateOfChange=\frac{-8}{4}$

On solving,

  $RateOfChange=-2$

Hence, rate of change in the interval $x=-1$ to $x=3$ is,

-2

For $x=0$ to $x=4$

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

  $y=3$

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

  $y=-5$

For the rate of change, substituting the value,

  $RateOfChange=\frac{-5-3}{4-0}$

So,

  $RateOfChange=\frac{-8}{4}$

On solving,

  $RateOfChange=-2$

Hence, rate of change in the interval $x=0$ to $x=4$ is,

-2