The function f(x)=x−−√ is reflected over the x-axis, translated 4 units down and 5 units to the left, then vertically stretched by a factor of 3. Which equation best represents the new function created?

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chefallen4540 chefallen4540 · Answer 1 · 2021-10-29T15:52:56+02:00

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MrRoyal MrRoyal · Answer 2 · 2021-11-03T18:01:59+01:00

Transformation involves changing the position of a function.

The equation of the new function is: [tex]\mathbf{g(x) = -3\sqrt{x + 5} - 12}[/tex]

The function is given as:

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

The rule of reflection across the x-axis is:

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

So, we have:

[tex]\mathbf{f'(x) = -\sqrt x}[/tex]

The rule of translation, 4 units down and 5 units left is:

[tex]\mathbf{(x,y) \to ( x + 5,y-4)}[/tex]

So, we have:

[tex]\mathbf{f"(x) = -\sqrt{x + 5} - 4}[/tex]

The rule of vertical stretch by a factor of # is:

[tex]\mathbf{(x,y) \to (x,3y)}[/tex]

So, we have:

[tex]\mathbf{g(x) = 3(-\sqrt{x + 5} - 4)}[/tex]

[tex]\mathbf{g(x) = -3\sqrt{x + 5} - 12}[/tex]

Hence, the equation of the new function is:

[tex]\mathbf{g(x) = -3\sqrt{x + 5} - 12}[/tex]