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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 the parent graph.

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

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

The given function is: $y=\sqrt{x+4}$

To graph a function, find a few coordinates by substituting values of ‘$x$’ and find finding the respective values of ‘$y$’.

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=−4,\\ y=\sqrt{−2+4}\\ =\sqrt{0}\\ =0\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=−3,\\ y=\sqrt{−3+4}\\ =\sqrt{1}\\ =1\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=0,\\ y=\sqrt{0+4}\\ =\sqrt{4}\\ =2\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=5,\\ y=\sqrt{5+4}\\ =\sqrt{9}\\ =3\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=12,\\ y=\sqrt{12+4}\\ =\sqrt{16}\\ =4\end{array}$

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

The parent function $y=\sqrt{x+4}$is the simplest square root function.

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

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

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

The value 4 is added inside the square root of the parent function $y=\sqrt{x}$. So the graph$y=\sqrt{x+4}$ is the translation of the parent graph $y=\sqrt{x}$.

Since 4 is added inside the root, the graph is translated to the left by 4 units.

Since the values inside the root must be positive.

$x+4â‰\yen 0$

Adding ‘$-4$’ on both sides.

$\begin{array}{c}x+4−4â‰\yen 0−4\\ x+0â‰\yen −4\\ xâ‰\yen −4\end{array}$

$xâ‰\yen −4⇒x∈[−4,∞)$

Therefore, domain: $[−4,∞)$

The $y$values are $\sqrt{x+4}$. 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:$[0,∞)$