Question

Using correct vocabulary such as vertical translation (up/down), horizontal translation (right/left), verticalstretch, vertical compression, ×-axis reflection, and y-axis reflection including specifics about the number ofunits, write in words how the following equation has changed from the parent function

Answer 1

To go from

`y=\sqrt[]{x}`

to

`y=2\sqrt[]{-x-5}+3.`

First, we reflect over the y-axis, and get:

`y=\sqrt[]{-x}\text{.}`

Second, we translate horizontally 5 units to the right, and get:

`y=\sqrt[]{-x-5}.`

Third, we stretch vertically by a scale factor of 2, and get:

`y=2\sqrt[]{-x-5}.`

Finally, we translate vertically 3 units up, and get:

`y=2\sqrt[]{-x-5}+3`

Answer: The function is reflected over the y-axis, translated horizontally 5 units to the right, stretched vertically by a scale factor of 2, and finally translated vertically 3 units up.