MATH SOLVE

4 months ago

Q:
# 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 rightstretched by a factor of 2, reflected over the x-axis, and translated 9 units leftstretched by a factor of 2, reflected over the y-axis, and translated 9 units rightstretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Accepted Solution

A:

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 9Therefore, 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.