Graph the function. Compare to the parent graph. State the domain and range.

$\mathit{y}\mathbf{=}\mathbf{-}\sqrt{\mathbf{x}}$

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 ‘$y$’.

$\begin{array}{c}\text{For\hspace{0.17em}\hspace{0.17em}}x=0,\\ y=-\sqrt{0}\\ =0\end{array}$

$\begin{array}{c}\text{For\hspace{0.17em}\hspace{0.17em}}x=1,\\ y=-\sqrt{1}\\ =-\left(1\right)\\ =-1\end{array}$

$\begin{array}{c}\text{For\hspace{0.17em}\hspace{0.17em}}x=4,\\ y=-\sqrt{4}\\ =-\left(2\right)\\ =-2\end{array}$

$\begin{array}{c}\text{For\hspace{0.17em}\hspace{0.17em}}x=9,\\ y=-\sqrt{9}\\ =-\left(3\right)\\ =-3\end{array}$

$\begin{array}{c}\text{For\hspace{0.17em}\hspace{0.17em}}x=16,\\ y=-\sqrt{16}\\ =-\left(4\right)\\ =-4\end{array}$

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, $x\ge 0,\Rightarrow x\in [0,\infty )$.

Therefore, domain: $[0,\infty )$

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,$y\le 0,\Rightarrow y\in (-\infty ,0]$

Therefore, Range:$(-\infty ,0]$