Question

Which of the following describes the graph of y = StartRoot negative 4 x minus 36 EndRoot 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

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

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:

$f(x)=\sqrt x$

Transformed function is given as:

$y=g(x)=\sqrt{-4x-36}=\sqrt{-4(x+9)}=2\sqrt{-(x+9)}$

Now, let us transform $f(x)$ to $g(x)$ in steps.

1. First we will multiply 2 to 'f(x)'. So, $\sqrt{x}\to 2\sqrt{x}$

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.

$2\sqrt x\to 2\sqrt{-x}$

This reflects the function over the y-axis.

3. Now, we add 9 to the 'x' value of the above function.

$2\sqrt{-x}\to 2\sqrt{-(x+9)}$

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.