Let $$ f(x)=3 \sqrt{x} $$. If $$ g(x) $$ is the graph of $$ f(x) $$ shifted up 6 units and right 2 units, write a formula for $$ g(x) $$. $$ g(x)=\square $$ Enter $$ \sqrt{x} $$ as sqrt(x).

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To find the formula for $$ g(x) $$, we need to apply the transformations to the function $$ f(x) = 3 \sqrt{x} $$.

1. **Shift up 6 units**: This means we add 6 to the function. So, the new function becomes:
   $$
   f(x) + 6 = 3 \sqrt{x} + 6
   $$

2. **Shift right 2 units**: To shift a function to the right by $$ h $$ units, we replace $$ x $$ with $$ x - h $$. In this case, $$ h = 2 $$. Therefore, we replace $$ x $$ with $$ x - 2 $$:
   $$
   g(x) = 3 \sqrt{x - 2} + 6
   $$

Putting it all together, the formula for $$ g(x) $$ is:
$$
g(x) = 3 \sqrt{x - 2} + 6
$$

Thus, the final answer is:
$$
g(x) = 3 \sqrt{x - 2} + 6
$$
$$ g(x) = 3 \sqrt{x - 2} + 6 $$

Let \( f(x)=3 \sqrt{x} \). If \( g(x) \) is the graph of \( f(x) \) shifted up 6 units and right 2 units, write a formula for \( g(x) \). \( g(x)=\square \) Enter \( \sqrt{x} \) as sqrt(x).

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