Chapter 3.6, Problem 2Q

Solution

To Graph: The function $y=\sqrt{x}+3$ and also state the domain and range.

Given information:

The function is $y=\sqrt{x}+3$ .

Graph:

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

Substitute the values of x into the function $y=\sqrt{x}+3$ to find the values of y ,

Put $x=0$ into $y=\sqrt{x}+3$ ,

  $\begin{array}{l}y=\sqrt{0}+3\\ y=3\end{array}$

Now substitute $x=2$ into $y=\sqrt{x}+3$ ,

  $\begin{array}{l}y=\sqrt{2}+3\\ y=1.4142+3\\ y=4.4142\end{array}$

Now substitute $x=4$ into $y=\sqrt{x}+3$ ,

  $\begin{array}{l}y=\sqrt{4}+3\\ y=2+3\\ y=5\end{array}$

The resultant table is:

x	$y=\sqrt{x}+3$
0	3
2	4.4142
4	5
6	5.549

Now consider the above table and draw the graph:

  

Interpretation: The graph of equation $y=\sqrt{x}+3$ is passing through the points $\left(0,3\right),\left(2,4.414\right)\text{and}\left(6,5.449\right)$ .

The domain of the function $y=\sqrt{x}+3$ is $x\ge 0$ and its range is $y\ge 3$.