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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: $h\left(x\right)=\sqrt{x+3}$

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

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=−3,\\ h\left(−3\right)=\sqrt{−3+3}\\ =\sqrt{0}\\ =0\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=−2,\\ h\left(−2\right)=\sqrt{−2+3}\\ =\sqrt{1}\\ =1\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=1,\\ h\left(1\right)=\sqrt{1+3}\\ =\sqrt{4}\\ =2\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=6,\\ h\left(6\right)=\sqrt{6+3}\\ =\sqrt{9}\\ =3\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=13,\\ h\left(13\right)=\sqrt{13+3}\\ =\sqrt{16}\\ =4\end{array}$

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

The parent function of$h\left(x\right)=\sqrt{x+3}$ is the simplest square root function.

That is,$h\left(x\right)=\sqrt{x}$

The graph of parent function$h\left(x\right)=\sqrt{x}$ is given below.

Note: Since the parent function is just used for comparison, it is graphed using graphing calculator.

The value 3 is added inside square root of parent function $h\left(x\right)=\sqrt{x}$. So the graph $h\left(x\right)=\sqrt{x+3}$ is the translation of the parent graph $h\left(x\right)=\sqrt{x}$.

Since 3 is added inside the root, the graph is translated to the left by 3 units.

Since the values inside the root must be positive.

$x+3â‰\yen 0$

Adding ‘$-3$’ on both the sides.

$\begin{array}{c}x+3−3â‰\yen 0−3\\ x+0â‰\yen −3\\ xâ‰\yen −3\\ x=0\end{array}$

$xâ‰\yen −3⇒x∈[−3,∞)$

Therefore, domain:$[−3,∞)$

The h(x)values are square root of $x+3$. As square roots are positive, $h\left(x\right)$takes all the positive real values including zero.

Therefore,$h\left(x\right)â‰\yen 0,\text{ â¶Ä‰â¶Ä‰}⇒h\left(x\right)∈[0,∞)$

Therefore, Range:$[0,∞)$