Finding the y-intercept of a transformed function

An algebra teacher is exploring the properties of linear functions. She has a function given by the equation:

$$ f(x) = 4x - 7 $$

According to the teacher, she adds a constant $$ k $$ to the output of this function, creating a new function:

$$ g(x) = f(x) + k $$

She then states that the intercept of the graph of $g(x)$ can be expressed as a function of the constant $$ k $$.

What is the $y$-intercept of the function $$ g(x) $$ in terms of $$ k $$?