To determine the vertical shift of the function \( f(x) = \log_3(x) + 681 \) as compared to its parent function \( g(x) = \log_3(x) \), we need to examine how the function has been altered.
The parent function \( g(x) = \log_3(x) \) has no vertical shift. When we look at \( f(x) \):
\[ f(x) = \log_3(x) + 681 \]
This indicates that the function has been shifted vertically upward by 681 units.
Therefore, the correct response regarding the vertical shift in comparison to the parent function \( \log_3(x) \) is:
681 units up.
However, this option isn't present in your list. If you were initially referring to a different version of the function and a vertical shift of 681 seems incorrect, please clarify the original function for accurate analysis.