Understanding log-log axes
But what happened to the graph for ω &lt; 0 ?


A log scaled axis can't show the range \$\omega &lt; 0\$, because the logarithm function isn't defined (or if you do define it, isn't real valued) for arguments less than or equal to zero.

If this is a real filter (real-valued inputs and outputs) then you know that the response to negative frequencies is the complex conjugate of the response to positive frequencies, so graphing the negative frequencies doesn't give you any new information and isn't necessary.