Definition: Every decimal ending in a string of 9's is equal to another ending in a string of 0's (e.g., $1.23999\ldots=1.24000\ldots$). Here use one ending in $9$s.
Considering the above definition which graph is true?
Graph #1:
Graph #2:
I think the first one is true. for example consider $-0.1\leq x<0$:
$x=-0.1=-0.099999 \Longrightarrow f(x)=0$
what do you think?
Thanks.
Agreed. Your counterexample shows #2 is not possible. It is easy to see #1 accurately pictures what's happening by letting $x = y+\epsilon$ where $\epsilon \in (0,1)$, and it should map to $y$, as it is in #1.