Question

Hello! I need some assistance with this homework question, pleaseQ19

Answer 1

We start with the parent function:

`y=\sqrt[]{x}`

The transformations are:

• Shift up 6 units

,

• Reflect about the x-axis

,

• Reflect about the y-axis

The first transformation is equal to add 6 units to y:

`\begin{gathered} y_2=y+6 \\ y_2=\sqrt[]{x}+6 \end{gathered}`

Then, a reflection across the x-axis makes y change sign, so we will have:

`\begin{gathered} y_3=-y_2 \\ y_3=-\sqrt[]{x}-6 \end{gathered}`

Finally, a reflection across the y-axis makes the argument x change sign, so we will have:

`\begin{gathered} y_4=y_3(-x) \\ y_4=-\sqrt[]{-x}-6 \end{gathered}`

This is the final function.

We can graph this function, and the intermediate steps, as:

Answer: y = -√-x - 6