Graph the function, and compare to the parent graph. State the domain and range.

$y=\sqrt{x}+5$

Parent graph:The simplest form of the given function is called the parent function of that function and the graph of the parent function is called parent graph.

Domain: The set of all possible values for which given function defined is called domain.

Range: The set of all possible values of the given function is called range.

The given function is:$y=\sqrt{x}+5$

In order to graph a function, find few co-ordinates by substituting values of ‘x’ and find finding the respective values of ‘y’.

$$\begin{gathered} \text{For\hspace{0.17em}\hspace{0.17em}}x=0, \\ y=\sqrt{0}+5 \\ =0+5 \\ =5 \end{gathered}$$

$$\begin{gathered} \text{For\hspace{0.17em}\hspace{0.17em}}x=1, \\ y=\sqrt{1}+5 \\ =1+5 \\ =6 \end{gathered}$$

$$\begin{gathered} \text{For\hspace{0.17em}\hspace{0.17em}}x=4, \\ y=\sqrt{4}+5 \\ =2+5 \\ =7 \end{gathered}$$

$$\begin{gathered} \text{For\hspace{0.17em}\hspace{0.17em}}x=9, \\ y=\sqrt{9}+5 \\ =3+5 \\ =8 \end{gathered}$$

$$\begin{gathered} \text{For\hspace{0.17em}\hspace{0.17em}}x=16, \\ y=\sqrt{16}+5 \\ =4+5 \\ =9 \end{gathered}$$

Plot these co-ordinates on a coordinate plane and join those points to get the required graph.

The parent function of $y=\sqrt{x}+5$is $y=\sqrt{x}$

The value 5 is being added to the parent function$y=\sqrt{x}$ a value greater than 1. So the graph is translated up 5 units from the parent graph $y=\sqrt{x}$.

Since ‘x’ is inside the root, the values inside the root must be positive.

Therefore, values of x is all positive real numbers including zero.

That is, $x\ge 0,\Rightarrow x\in [0,\infty )$.

Therefore, domain:$[0,\infty )$

Since the y-values are added by 5. So y takes all the positive real values starting from 5, including 5.

Therefore,$y\ge 5,\Rightarrow y\in [5,\infty )$

Therefore, Range:$[5,\infty )$