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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:$y=\sqrt{x+4}$

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

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

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

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

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

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

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

The parent function of$y=\sqrt{x+4}$ is$y=\sqrt{x}$

The value 4 is being added to the square root of parent function $y=\sqrt{x}$. So the graph is translated 4 units left from the parent graph $y=\sqrt{x}$.

Since the values inside the root must be positive.

$x+4â‰\yen 0$

Adding ‘$-4$’ on both the sides.

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

Therefore, domain:$[−4,\mathrm{∞})$

Since the y-values square root of $x+4$. As principal square roots are positive, y takes all the positive real values including zero.

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

Therefore, Range:$[0,\mathrm{∞})$