Answer:
[tex]y=- \sqrt{\dfrac{1}{2}x}[/tex]
Step-by-step explanation:
Parent functions are the simplest form of a given family of functions.
Transformations of graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
Transformations
[tex]\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a \\ & \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a \\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a \end{aligned}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
Given parent function:
[tex]y=\sqrt{x}[/tex]
Horizontal stretch:
As this is a horizontal stretch, the x variable should be multiplied by a value between zero and 1:
[tex]\implies y= \sqrt{\dfrac{1}{2}x}[/tex]
Reflected in the x-axis:
To reflect a function in the x-axis, simply make the function negative:
[tex]\implies y=- \sqrt{\dfrac{1}{2}x}[/tex]
