Cars lights go dim or won't work,radio stops working, air stops w

Had car at mechanics car would not start had to be jumped. While driving the car the lights go dim or stop working the radio won't work and the air won't work Mechanic said he checked everything can't find the problem. he said can't find anything wrong with the car. Took the car home. my daughter drove it over a friends house when she went to leave car would not start had to jump it again. drove home I went to take car for a ride would not start. mechanic said battery and alternator were fine i don't know what else to do just bought the car at the end of nov. it only has 54000 miles car is a piece of ****