Chapter 2, Problem 128CR

To determine

To graph: the function $g(x)$ and compare it with the graph $f(x)$ .

Answer to Problem 128CR

The quantity increases or decreases, exponentially it increases or decreases with the same percent over equal period of time.

Explanation of Solution

Given information: $\begin{array}{l}f(x)=\frac{1}{x}\\ g\left(x\right)=\frac{-1}{x+2}-2\end{array}$

Graph:

graph of $g(x)$ is given below by assuming the value of x and keep that value in the function to get the value of y coordinates:

  

  

Now comparing with the graph $f(x)$ it is shown as:

  

Interpretation : Observing from the graph, let $y=g\left(x\right)=\frac{-1}{x+2}-2$ and at $x=0$

  $y=g\left(0\right)=\frac{-1}{0+2}-2=-2.5$

Hence the co ordinates of graph $g(x)$ is $\left(0,-2.5\right)$

Now , plot the graph $f(x)$ by assuming the value of x

Now comparing both the graph at the point of intersection the value of $x$ of $f(x)$ is $\left(-.382\right)$

Therefore $f(x)=\frac{1}{-.382}=-2.61$

We can say that as the quantity increases or decreases, exponentially it increases or decreases with the same percent over equal period of time.