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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:$y=−\sqrt{x}$

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

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

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

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

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

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

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

The parent function of$y=−\sqrt{x}$ is the simple square root function.

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

Using graphing calculator, 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 parent function is multiplied by ‘$-1$’, a value less than 0. So the graph is a reflection of $y=\sqrt{x}$ across the $X$-axis.

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: $[0,∞)$

Since the square root ofx-values are multiplied by ‘$-1$’$y$takes all the negative real values including zero( as the starting point of graph is origin).

Therefore,$y≤0,\text{ â¶Ä‰â¶Ä‰}⇒y∈(−∞,0]$

Therefore, Range:$(−∞,0]$