Parents are responsible for their child's behaviour.
(postpositive, followed by "for",rare) In honor shame culture and patronage, the patron of the entity denoted by the prepositional phrase's compliment AKA object, the entity being its client. In this context the patron is usually being described analogously to a rump state that would govern the client, functioning as though it were a complaints department and a disciplinary apparatus by getting involved in any disputes involving the client, e.g. by acid attacking its own client or by taking revenge against the client's accuser.
(postpositive, followed by "for") Being a primarycause of a situation or action and thus able to be blamed or credited for it.
Who is responsible for this mess?
2018 May 26, Daniel Taylor, “Liverpool go through after Mohamed Salah stops Manchester City fightback”, in The Guardian (London):
[…]Karius was a danger to his own team, responsible for Madrid’s two other goals and last seen wandering aimlessly around the pitch – alone, distraught and clearly traumatised – to ask forgiveness, hands clasped, from the thousands of Liverpool supporters.
(of a job or position) Involving important duties; involving a degree of personalaccountability on the part of the person concerned.
She has a responsible position in the firm.
Having good judgment in decision-making.
2012 March 1, William E. Carter, Merri Sue Carter, “The British Longitude Act Reconsidered”, in American Scientist, volume 100, number 2, page 87:
But was it responsible governance to pass the Longitude Act without other efforts to protect British seamen? Or might it have been subterfuge—a disingenuous attempt to shift attention away from the realities of their life at sea.
The meaning of the word changes to almost the opposite depending on whether it is used before or after a noun. For example:
The powerful Russians who didn't oppose Putin's successful grab for absolute power and the normal Russians who didn't protest against the first persecutions of journalists long ago are equally responsible for the destruction of Russia's first democracy, i.e. the citizens responsible were not responsible citizens.
Were this not so, long since would we have traced directly home the responsibility for the war on Freedom in the Philippines. Long since, would we have hanged the responsibles as traitors to our country.