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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 ‘$y$’.

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

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

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

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

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

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 simple 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 graph$y=\sqrt{x}−2$ is obtained by parent function is subtracted by ‘2’.

Therefore, the graph$y=\sqrt{x}−2$ is translated(shifted) downward by 2 units from the origin, on comparing with 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, $xâ‰\yen 0,\text{ â¶Ä‰â¶Ä‰}⇒x∈[0,∞)$.

Therefore, domain:$[0,∞)$

In$y=\sqrt{x}−2$ the square root of xis subtracted by ‘2’.

As square root is always positive, the least value it takes is zero.

Find the starting value of $y$by substituting $x=0$in $y=\sqrt{x}−2$.

$\begin{array}{c}y=\sqrt{0}−2\\ =0−2\\ =−2\end{array}$

Also, in $y=\sqrt{x}−2$, coefficient of $\sqrt{x}$is 1, which is positive.

Therefore,localid="1648042921775" $y$ takes all the real values greater than or equal to ‘$-2$’.

That is,$yâ‰\yen −2,\text{ â¶Ä‰â¶Ä‰}⇒y∈[−2,∞)$

Therefore, Range:$[−2,∞)$