Question

Need help with this questionAnd I know it looks cropped but yes that is the full question

Answer 1

For

$y=\sqrt{-4x-36}$

when it changed from,

$y=\sqrt{x}$

the translation process as:

$\begin{gathered} y=\sqrt{-4x-36} \\ y=\sqrt{-4(x+9)} \\ y=2\sqrt{-(x+9)} \\ \Rightarrow y=2\sqrt{-x-9} \end{gathered}$

It stretched by a factor of 2,

$y=\sqrt{x}\rightarrow y=2\sqrt{x}$

Reflected over the y-axis

$y=2\sqrt{x}\rightarrow y=2\sqrt{-x}$

Translated 9units leftwards

$y=2\sqrt{-x}\rightarrow y=2\sqrt{-x-9}$

Hence, the fourth option is correct.