The graph of the function $$ y=f(x)+81 $$ can be obtained from the graph of $$ y=f(x) $$ by one of the following actions: shifting the graph of $$ f(x) $$ to the left 81 units shifting the graph of $$ f(x) $$ upwards 81 units shifting the graph of $$ f(x) $$ to the right 81 units shifting the graph of $$ f(x) $$ downwards 81 units

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The function $$ y = f(x) + 81 $$ indicates that the original function $$ f(x) $$ is being modified by adding 81 to its output values. This means that for every value of $$ x $$, the corresponding $$ y $$ value is increased by 81.
In function transformations, adding a constant to the function (like $$ +81 $$) results in a vertical shift. Specifically, adding a positive constant shifts the graph upwards.
Therefore, the graph of $$ y = f(x) + 81 $$ can be obtained from the graph of $$ y = f(x) $$ by shifting the graph upwards 81 units.
Shifting the graph of $$ f(x) $$ upwards 81 units.

The graph of the function

can be obtained from the graph of

by one of the following actions:
shifting the graph of to the left 81 units
shifting the graph of upwards 81 units
shifting the graph of to the right 81 units
shifting the graph of downwards 81 units

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The graph of the function can be obtained from the graph of by one of the following actions: shifting the graph of to the left 81 units shifting the graph of upwards 81 units shifting the graph of to the right 81 units shifting the graph of downwards 81 units