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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: $y=−2\sqrt{x}$

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

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

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

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

$\begin{array}{l}\text{¹ó´Ç°ù â¶Ä‰}x=9,\\ y=−2\sqrt{9}\\ =−2\left(3\right)\\ =−6\end{array}$

$\begin{array}{l}\text{¹ó´Ç°ù â¶Ä‰}x=16,\\ y=−2\sqrt{16}\\ =−2\left(4\right)\\ =−8\end{array}$

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

The parent function of $y=−2\sqrt{x}$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 ‘$-2$’.

On comparing with the parent function, the graph$y=−2\sqrt{x}$ is a vertical stretch of$y=\sqrt{x}$ (since the absolute value of ‘$-2$’ is 2 which is greater than 1) and a reflection across the $X$-axis (since the coefficient of$\sqrt{x}$ is ‘$-2$’ which is negative).

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: $[0,\mathrm{∞})$

In $y=−2\sqrt{x}$, the square root of $x$is multiplied by $-2$.

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

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

$\begin{array}{l}y=−2\sqrt{0}\\ =−2\left(0\right)\\ =0\end{array}$