Respuesta :
Answer:
Stretched by a factor of 2, reflected over the y-axis, and translated 9 units left.
Step-by-step explanation:
Given:
Parent function is given as:
[tex]f(x)=\sqrt x[/tex]
Transformed function is given as:
[tex]y=g(x)=\sqrt{-4x-36}=\sqrt{-4(x+9)}=2\sqrt{-(x+9)}[/tex]
Now, let us transform [tex]f(x)[/tex] to [tex]g(x)[/tex] in steps.
1. First we will multiply 2 to 'f(x)'. So, [tex]\sqrt{x}\to 2\sqrt{x}[/tex]
This stretches the function in the y direction by a factor of 2.
2. Now, we multiply the 'x' value of the above transformed function by -1.
[tex]2\sqrt x\to 2\sqrt{-x}[/tex]
This reflects the function over the y-axis.
3. Now, we add 9 to the 'x' value of the above function.
[tex]2\sqrt{-x}\to 2\sqrt{-(x+9)}[/tex]
Adding a positive number 9 to 'x' value shifts the graph to left by 9 units.
So, the complete transformation is:
Stretched by a factor of 2, reflected over the y-axis, and translated 9 units left.
Answer:
Stretched by a factor of 2, reflected over the y-axis, and translated 9 units left.
Step-by-step explanation:
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