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Which of the following describes the graph of y=\sqrt(-4x-36) compared to the parent square root function?
stretched by a factor of 2, reflected over the x-axis, and translated 9 units right
stretched by a factor of 2, reflected over the x-axis, and translated 9 units left
stretched by a factor of 2, reflected over the y-axis, and translated 9 units right
stretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Respuesta :

Answer:

Option D - Stretched by a factor of 2, reflected over the y-axis, and translated 9 units left.

Step-by-step explanation:

Given : The function [tex]y=\sqrt{-4x-36}[/tex]

To find : Which of the following describes the graph of [tex]y=\sqrt{-4x-36}[/tex]compared to the parent square root function?

Solution :

First we simplify the given expression

[tex]y=\sqrt{-4x-36}[/tex]

[tex]y=\sqrt{4(-x-9)}[/tex]

[tex]y=2\sqrt{-(x+9)}[/tex]

→When we see the original square root function minus was taken outside x and 9 was added from x and 2 was multiplied to the entire function.

  • Multiplying 2 in the function will give you the stretched by a factor of 2.
  • [tex]g(x)=\sqrt{-x}[/tex] shows the reflection about y-axis i.e, (x,y)→(-x,y).
  • If f(x)→f(x+b) then function is shifted left by unit b

        ⇒ g(x))→g(x+9) then function is shifted left by unit 9

Therefore, The graph of was stretched by a factor of 2, reflected over the y-axis, and translated 9 units left to obtain the graph of the function .

So, Option D is correct.

oddoaxel

Answer:

D) stretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Step-by-step explanation:

its right on edge

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