As I was removing the vacuum lines I broke one end of this check valve looking deal. Can someone tell me what is the use of this valve? Can I just bypass that with a vacuum hose?

 

Series four turbo? or non turbo? right or left side of the throttle body?

 

Non Turbo S4, Left of the throttle body.

 

That line runs to the double throttle diaphragm. You can probably just remove that whole line, and cap off the nipple on the thermo-valve (attached to the thermowax). Or you can remove both lines on the thermo-valve, and cap the nipple on the UIM. The double throttle diaphragm has almost definitely failed (I have yet to see a functional one), which means the outer set of throttle plates will just stay open 24/7. On a normally functioning S4 NA, the thermovalve allows vacuum to be applied to the diaphragm when the engine is cold. The valve you have in the picture is a delay valve that dampens the vacuum applied to the diapgram, which opens the outer throttle plates slowly when throttle is applied. But once the engine is warm (140ºF +), the plates will always be open. http://mazdarx7.iougs.com/intakeair.shtml

In the event that your double throttle diaphragm is still working (by some miracle), you could replace that hose & valve with a new piece of line, but you'll lose the delay feature. The throttle plates will snap open quickly with harsh throttle input (when cold). That would essentially be the same as disabling the system, since the delay was the whole point.

 

One source for a replacement: http://www.mazdatrix.com/b-egr.htm
(bottom of page).