Question 443245
{{{f(x) = sqrt(x)}}}

Here are some rules for translations:

If it's inside the parenthesis/root:
+  = left
-  = right
If it's outside the parenthesis/root:
+  = up
- = down

Reflect about the x axis:
g(x) = -f(x)

Reflect about the y axis:
g(x) = f(-x)

Reflect about the origin:
g(x) = -f(-x)

So using these rules, we should be able to construct a g(x):

If we are shifting left, then we add the amount inside of the root.

{{{g(x) = sqrt(x+6)}}}

In addition we are moving up 7, so {{{g(x) = sqrt(x+6)+7}}}

Finally, we are reflecting about the x axis so, {{{-g(x) = sqrt(x+6)+7}}}, which when we solve for g(x) gives us {{{-(sqrt(x+6) + 7)= -sqrt(x+6) - 7}}}

So we have {{{highlight(-sqrt(x+6) -7)}}}
Here is a graph so you can see the new translation.

{{{graph(600,600,-25,25,-25,25,sqrt(x), -sqrt(x+6)-7)}}}