The function $$ f $$ is defined as follows. $$ f(x)=5 x^{2}+1 $$ If the graph of $$ f $$ is translated vertically upward by 5 units, it becomes the graph of a function $$ g $$. Find the expression for $$ g(x) $$.

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Let the function be 
$$
f(x)=5x^2+1.
$$
To translate the graph of $$ f $$ vertically upward by 5 units, we add 5 to its output. This gives the new function 
$$
g(x)=f(x)+5.
$$
Substitute $$ f(x) $$ into the equation:
$$
g(x)=5x^2+1+5.
$$
Simplify the expression:
$$
g(x)=5x^2+6.
$$
$$ g(x) = 5x^2 + 6 $$

The function is defined as follows.

If the graph of is translated vertically upward by 5 units, it becomes the graph of a function .
Find the expression for .

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The function is defined as follows. If the graph of is translated vertically upward by 5 units, it becomes the graph of a function . Find the expression for .