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Identify all statements that are true when graphing the following square root function: f(x)=-√x-2 + 3

I. The horizontal shift is left 2 spaces.
II. The vertical shift is up 3 spaces.
III. The square root graph will flip.
IV. The square root graph will stretch by a factor of 2.

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Answer:

II. The vertical shift is up 3 spaces.

III. The square root graph will flip.

Step-by-step explanation:

The given equation is;

[tex]f(x) = - \sqrt{x - 2} + 3[/tex]

From the given function, we deduce the parent function to be:

[tex]g(x) = \sqrt{x} [/tex]

So we can see that the transformation is of the form.

[tex]f(x) = - g(x - 2) + 3[/tex]

So there is a horizontal shift of 2 units to the right.

There is a vertical upward shift by 2 units.

There is also a reflection in the x-axis, so the parent graph will flip.

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