\#2 i Let $$ f(x)=|x|+6 $$. Write a function $$ g $$ whose graph is a translation 5 units left of the graph of $$ f $$ The translated function is $$ g(x)=\square $$.

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To translate the graph of the function $$ f(x) = |x| + 6 $$ five units to the **left**, you need to adjust the input $$ x $$ by adding 5. This is because shifting left involves moving in the negative direction on the $$ x $$-axis.

Here's how you can do it:

1. **Original Function:**
   $$
   f(x) = |x| + 6
   $$

2. **Translation 5 Units Left:**
   To shift the graph 5 units to the left, replace $$ x $$ with $$ x + 5 $$:
   $$
   g(x) = |x + 5| + 6
   $$

So, the translated function is:
$$
g(x) = |x + 5| + 6
$$

**Answer:**  
After simplifying, the translated function is $$ g(x) =\, |\,x + 5\,|\, +\, 6 $$.
The translated function is $$ g(x) = |x + 5| + 6 $$.

\#2 i Let \( f(x)=|x|+6 \). Write a function \( g \) whose graph is a translation 5 units left of the graph of \( f \) The translated function is \( g(x)=\square \).

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