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

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

Explanation:

took test

Answer 2

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

Explanation:

Given:

Parent function is given as:

`f(x)=\sqrt x`

Transformed function is given as:

`y=g(x)=√(-4x-36)=√(-4(x+9))=2√(-(x+9))`

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

1. First we will multiply 2 to 'f(x)'. So,
`√(x)\to 2√(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√(-x)`

This reflects the function over the y-axis.

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

`2√(-x)\to 2√(-(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.