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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: $y=\sqrt{x}−1$

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

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

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

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

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

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=16,\\ y=\sqrt{16}−1\\ =4−1\\ =3\end{array}$

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

The parent function$y=\sqrt{x}−1$ is the simple 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 graph$y=\sqrt{x}−1$ is obtained by the parent function is subtracted by ‘1’.

Therefore, the graph$y=\sqrt{x}−1$ is translated(shifted) downward by 1 unit 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$x$are all positive real numbers including zero.

That is, $xâ‰\yen 0,\text{ â¶Ä‰â¶Ä‰}⇒x∈[0,∞)$.

Therefore, domain: $[0,∞)$

The square root of $x$is subtracted by ‘1’.

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

Find the starting value of $y$ by substituting $x=0$in $y=\sqrt{x}−1$.

$\begin{array}{c}y=\sqrt{0}−1\\ =0−1\\ =−1\end{array}$

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

Therefore,y takes all the real values greater than or equal to ‘$-1$’.

That is,$yâ‰\yen −1,\text{ â¶Ä‰â¶Ä‰}⇒y∈[−1,∞)$

Therefore, Range:$[−1,∞)$