Chapter 3.6, Problem 3Q

Solution

To Graph: The function $g\left(x\right)=\sqrt{x+2}-5$ and also state the domain and range.

Given information:

The function is $g\left(x\right)=\sqrt{x+2}-5$ .

Graph:

For drawing the graph first find the coordinates with the help of the given function.

Substitute the values of x into the function $g\left(x\right)=\sqrt{x+2}-5$ to find the values of y ,

Let’s take $y=g\left(x\right)$ .

Now Put $x=-2$ into $y=\sqrt{x+2}-5$ ,

  $\begin{array}{l}y=\sqrt{-2+2}-5\\ y=-5\end{array}$

Now substitute $x=0$ into $y=\sqrt{x+2}-5$ ,

  $\begin{array}{l}y=\sqrt{0+2}-5\\ y=1.4142-5\\ y=-3.5858\end{array}$

Now substitute $x=2$ into $y=\sqrt{x+2}-5$ ,

  $\begin{array}{l}y=\sqrt{2+2}-5\\ y=2-5\\ y=-3\end{array}$

The resultant table is:

x	$y=\sqrt{x+2}-5$
$-2$	$-5$
0	$-3.586$
2	$-3$
7	$-2$

Now consider the above table and draw the graph:

  

Interpretation: The graph of equation $g\left(x\right)=\sqrt{x+2}-5$ is passing through the points $\left(-2,-5\right),\left(0,-3.586\right),\left(2,-3\right)\text{and}\left(7,-2\right)$ .

The domain of the function $g\left(x\right)=\sqrt{x+2}-5$ is $x\ge -2$ and its range is $y\ge -5$.