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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: $y=\sqrt{x−1.5}$

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

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=1.5\\ y=\sqrt{1.5−1.5}\\ =\sqrt{0}\\ =0\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=2.5,\\ y=\sqrt{2.5−0.5}\\ =\sqrt{1}\\ =1\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=5.5,\\ y=\sqrt{5.5−1.5}\\ =\sqrt{4}\\ =2\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=10.5,\\ y=\sqrt{10.5−1.5}\\ =\sqrt{9}\\ =3\end{array}$

$\begin{array}{c}\text{¹ó´Ç°ù â¶Ä‰}x=17.5,\\ y=\sqrt{17.5−1.5}\\ =\sqrt{16}\\ =4\end{array}$

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

The parent function$y=\sqrt{x−1.5}$ is the simplest 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 value 1.5 is subtracted inside the square root of the parent function $y=\sqrt{x}$. So the graph$y=\sqrt{x−1.5}$ is the translation of the parent graph $y=\sqrt{x}$.

Since 1.5 is subtracted inside the root, the graph is translated to the right by 1.5 units.

Since the values inside the root must be positive.

$x−1.5â‰\yen 0$

Adding ‘1.5’ on both sides.

$\begin{array}{c}x−1.5+1.5â‰\yen 0+1.5\\ x+0â‰\yen 1.5\\ xâ‰\yen 1.5\end{array}$

$xâ‰\yen 1.5⇒x∈[1.5,∞)$

Therefore, domain: $[1.5,∞)$

The $y$values are the square root of $x−1.5$. As square roots are positive$y$ takes all the positive real values including zero.

Therefore,$yâ‰\yen 0,\text{ â¶Ä‰â¶Ä‰}⇒y∈[0,∞)$

Therefore, Range:$[0,∞)$