A way to counter Rengar, and most invis champs: Pink wards.
Being seen by pink wards causes most champs that can go invisible to have their bonuses: of bonus armor pen, magic pen, damage ,shield, attack speed, etc, if they are seen; removed.**Normal wards and blue wards DO NOT GET RID OF THEIR STEALTH BONUSES THE ONLY ONES (I know of) ARE PINK
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Rengar's WHOLE ULT is trashed if he can be seen before he attacks. Plopping down a pink ward when you KNOW you can see them or know they are coming to your lane will negate most/all their invis bonuses. Same with any invisible attacks. HE's also an assassin he can one shot nearly ALL ADC's especially Kalista as she to my knowledge is almost as low hp as Kindred. If he goes AD he WILL one shot/two shot every squishy unless stunned regardless if he's invisible or not if he is full build.
Rengar's whole ult goes down onto cooldown once this is done, Twitch's attack speed stuff and extra damage is negated as as soon as he comes out of his invisible state he gets it; but when a pink is used you can get rid of that bonus as "now the enemies can see you". Just like Shaco with his invisible trick, his extra damage is negated once seen.
That's why some supports put a pink down after they see a rengar, Eve, twitch, or shaco go invisible in a bush as it will negate their damages and bonuses; making it easier to defend, even if it negates only a little damage.
So I would recommend next time an enemy champ can go invisible add pink wards, even if you are not a support, to your start game or throughout the game. Ward next to your tribush, near crugs if you're bot map, near gromp i you're on the topside of the map team, near the tribush if you're top on either side or later game near buffs. If you don't place one down but know/see a champ that can go invisible near you place it down and it reveals them so long as it is up. They have to either continue with their kill plan, or get rid of the ward or their invisible bonuses have no effect.
Now Teemo...If top vs a Teemo place a pink in the bush closest to tower so if you back he has to focus on getting rid of that ward or he can't go in that bush to trick you into going into it. Normally by the time you TP up there you can replace the ward with another pink ward and he has to do it over again. IT also reveals any shrooms in the bush he placed but only in the area it can see. I am pretty sure pinks negate his speed and damage as well but PLEASE KEEP IN MIND MY INFO IS FRO BEFORE THE WARD UPDATE AND U MIGHT HAVE CHANGED A BIT
Some people say pink reveals teemo, some say it doesnt, some say it reveals his shrooms and sometimes it doesnt so take this with a grain of salt and I hope this helps TuT;
Owl
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TLDR Pink wards make invisible champs revealed and negates stealth bonuses.**