Suppose you're given a DFA $M$ with a 5 tuple of $(Q, \Sigma, \delta, q_0, F)$.
How do you construct an NFA that accepts $L(M)$ and $\{\varepsilon\}$, the set containing the empty string? I know that a DFA is an NFA.
My thought is that you would simply add a new transition from the start state to the accepting state, which takes epsilon/the empty string.
For example (eps. is epsilon/empty string):
Since I've added an empty string transition, the machine is no longer a DFA, but it is an an NFA.