$$ f(x)=x^{2} $$ $$ g(x)=(x-g)^{2}+3 $$ We can thirki of $$ g $$ as a translated (shifted) version of $$ f $$. Complete the description of the transformation. Use nonnegative numbers. To get the function $$ g $$, shift $$ f $$ up/down $$ \vee $$ by $$ \square $$ units and to the right/left $$ v $$ by units.

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To describe the transformation from the function $$ f(x) = x^2 $$ to the function $$ g(x) = (x - g)^2 + 3 $$, we need to analyze the changes made to the original function.

1. **Vertical Shift**: The term $$ +3 $$ in $$ g(x) $$ indicates a vertical shift. Since it is positive, the function $$ f(x) $$ is shifted upwards by 3 units.

2. **Horizontal Shift**: The term $$ (x - g) $$ indicates a horizontal shift. The function is shifted to the right by $$ g $$ units. However, since $$ g $$ is a variable and not a specific number, we cannot assign a specific nonnegative number to this shift without additional information about $$ g $$.

Now, we can complete the description of the transformation:

To get the function $$ g $$, shift $$ f $$ up/down **by** $$ 3 $$ units and to the right/left **by** $$ g $$ units.

Thus, the completed description is:
- Shift $$ f $$ up by $$ 3 $$ units.
- Shift $$ f $$ to the right by $$ g $$ units.
To get the function $$ g $$, shift $$ f $$ up by 3 units and to the right by $$ g $$ units.

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