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TheSandman1337
We will try to approach it generally. If we have a function y=f(x) and we have then y=f(2x), then the graph of the function will be horizontally compressed. If we take f(x/2), the graph of the function will be dilated. (To get horizontal shifts, we need f(x+a), which is not the case here; for example [tex] \sqrt{x+4} [/tex] is horizontally shifted relative to its parent function). If we consider -y=f(x), then the graph of this new function is the graph of the parent function flipped along the x-axis. If we consider y=f(-x) (which is the case here, since [tex] \sqrt{-x} = \sqrt{(-x)} [/tex]) we have that the graph of the new function is the same as the old graph, just flipped along the y-axis. Each of those transformations is independent; combining our observations we see that the last answer is the correct one.
MrRoyal

The graph of [tex]y = \sqrt{-2x[/tex] relates to its parent function as a result of (d) horizontal compression by a factor of 2, and a reflection across the y-axis

What is a function transformation?

A function transformation involves changing the form or equation of a function to another through reflection, dilation, translation or rotation

How to determine the function transformation

The parent function is given as:

[tex]y = \sqrt x[/tex]

Compress the function horizontally by a factor of 2, using the following rule

[tex](x,y) \to (2x,y)[/tex]

So, we have:

[tex]y = \sqrt {2x[/tex]

Next, reflect the function over the y-axis, using the following rule

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]y = \sqrt {-2x[/tex]

Hence, the function transformation is (d)

Read more about function transformation at:

https://brainly.com/question/1548871

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