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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’.

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

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

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

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

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

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

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

The parent function is multiplied by ‘$-1$’, a value less than 0. So the graph is a vertical stretch of$y=\sqrt{x}$ and a reflection 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, $xâ‰\yen 0,\text{ â¶Ä‰â¶Ä‰}⇒x∈[0,\mathrm{∞})$.

Therefore, domain:$[0,\mathrm{∞})$

Since the y-values are multiplied by ‘$-1$’ y takes all the negative real values including zero.

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

Therefore, Range:$(−\mathrm{∞},0]$