An air purifier has two main functions that make it work: a fan and a filter. If both of these functions are in good working order, the air purifier should be working. To check that the fan is working, place a piece of tissue paper near the intake in the back - if it sticks, then the fan is working properly. Finally, take a look at the HEPA filters to see if it needs replacing - as long as it isn't caked in dust, and air can flow through it freely, your air purifier is working.