Question

I'm confused with how to start this off.It's function graphs, (square root) algebra 2My homeschool teacher didn't clarify

Answer 1

The preimage (Red) has the form of the square root function, but you need to translate it to 3 units to the left and 3 units down.

The square root function is:

`f(x)=\sqrt[]{x}`

In order to do the translation 3 units left, you need to add 3 inside of the parent function:

`f(x)=\sqrt[]{x+3}`

Now, to translate it vertically, you need to subtract 3 on the outside of the square root function:

`f1(x)=\sqrt[]{x+3}-3`

If you graph this function, you will prove that this is the pre-image (red) function on your question:

Now, to find the image (green function), you need to translate the pre-image 6 units up (you can do this by subtracting 6 from the inside of the parent function), and 6 units to the right (you have to add 6 outside of the square root), thus, the function will look like:

`\begin{gathered} f2(x)=\sqrt[]{x+3-6}-3+6 \\ f2(x)=\sqrt[]{x-3}+3 \end{gathered}`

And this is the graph of the pre-image and image: