Recall that :
1) A function
[tex]f\mleft(x\mright)[/tex]translated n-units to the left is
[tex]f\mleft(x-n\mright).[/tex]2) A function
[tex]h\mleft(x\mright)[/tex]translated m-units up is:
[tex]h\mleft(x\mright)+m.[/tex]3) A function g(x) reflected over the x-axis is:
[tex]-g(x)\text{.}[/tex]The parent function is:
[tex]y=\sqrt[]{x}\text{.}[/tex]The function of the graph of the above function translated horizontally 3 units to the left is:
[tex]y=\sqrt[]{x+3}.[/tex]The function of the graph of the above function translated vertically 4 units up is:
[tex]y=\sqrt[]{x+3}+4.[/tex]The function of the graph of the above function reflected over the x-axis is:
[tex]y=-(\sqrt[]{x+3}+4)=-\sqrt[]{x+3}-4.[/tex]Finally, the function of the graph of the above function stretched vertically by a scale factor of 2 is:
[tex]y=-2\sqrt[]{x+3}-4.[/tex]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.