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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: $y=\sqrt{x+2}$

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

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=−2,\\ y=\sqrt{−2+2}\\ =\sqrt{0}\\ =0\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=−1,\\ y=\sqrt{−1+2}\\ =\sqrt{1}\\ =1\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=2,\\ y=\sqrt{2+2}\\ =\sqrt{4}\\ =2\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=7,\\ y=\sqrt{7+2}\\ =\sqrt{9}\\ =3\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=14,\\ y=\sqrt{14+2}\\ =\sqrt{16}\\ =4\end{array}$

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

The parent function of $y=\sqrt{x+2}$is the simplest square root function.

That is, $y=\sqrt{x}$

The graph of parent function $y=\sqrt{x}$is given below.

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

The value 2 is added inside square root of parent function $y=\sqrt{x}$. So the graph$y=\sqrt{x+2}$ is the translation of the parent graph $y=\sqrt{x}$.

Since 2 is added inside the root, the graph is translated to the left by 2 units.

Since the values inside the root must be positive.

$x+2â‰\yen 0$

Adding ‘$-2$’ on both the sides.

$\begin{array}{c}x+2−2â‰\yen 0−2\\ x+0â‰\yen −2\\ xâ‰\yen −2\end{array}$

$xâ‰\yen −2⇒x∈[−2,∞)$

Therefore, domain: $[−2,∞)$

The $y$values are square root of $x+2$. As square roots are positive$y$ takes all the positive real values including zero.

Therefore,$yâ‰\yen 0,\text{ â¶Ä‰â¶Ä‰}⇒y∈[0,∞)$

Therefore, Range:$[0,∞)$