Question

What did I do wrong? Need help with this equation

Answer 1

Recall that :

1) A function

`f\mleft(x\mright)`

translated n-units to the left is

`f\mleft(x-n\mright).`

2) A function

`h\mleft(x\mright)`

translated m-units up is:

`h\mleft(x\mright)+m.`

3) A function g(x) reflected over the x-axis is:

`-g(x)\text{.}`

The parent function is:

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

The function of the graph of the above function translated horizontally 3 units to the left is:

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

The function of the graph of the above function translated vertically 4 units up is:

`y=\sqrt[]{x+3}+4.`

The function of the graph of the above function reflected over the x-axis is:

`y=-(\sqrt[]{x+3}+4)=-\sqrt[]{x+3}-4.`

Finally, the function of the graph of the above function stretched vertically by a scale factor of 2 is:

`y=-2\sqrt[]{x+3}-4.`

Answer:

The graph of the function has a horizontal translation Left 3 and vertical translation Up 4. The graph has been reflected over the x-axis and has been Vertically stretched.