y=2x²+4x+2-7
=2(x+1)²-7
-3<=x<=-1,则-2<=x+1<=0
则0<=(x+1)²<=4
2*0-7<=2(x+1)²-7<=2*4-7=1
-7<=2(x+1)²-7<=1
-10所以0<(x+1)²<9
2*0-7<2(x+1)²-7<2*9-7
-7<2(x+1)²-7<11
所以-7<=y<11