Jax should look to slow push the first and second waves and fast push the third wave then either cheater recall, get vision, or rotate. You should harass jax when he attempts to build the slow push but respect his lvl 2 advantage. Moreover, when the wave bounces back toward jax you should look for heavier trades if you have jungle vision and if he stayed. If you can get push in the lane you can harass him with q1s and play with your own minion wave when he jumps on you for a favorable trade. You can try to cheater recall if your jungle is pathing away and their jungle is pathing up in order to avoid a gank timer, or play for the 1v1 and get vision to guarantee you cannot get ganked.

Always avoid the stun from his e by spacing or using your e to dash out when he q's onto you.Do not walk in for a passive auto if jax is healthy and has counterstrike up.

Look to poke jax with q1 freely when he goes to farm. If he jumps onto you with his q then kite him using your w instantly and q2 + e backwards. Jax can only effectively trade with you with his counterstrike which has a 15 second cooldown early on. If his counterstrike is down and he walks up then you can combo him without much retaliation. Do not greed for passive procs on jax when he has lethal tempo stacked up.