If we transform each of the points we have
[tex]f(-2)=2(-2)^2+(-2)-1 = 8-2-1=5[/tex]
[tex]f(-1)=2(-1)^2+(-1)-1 = 2-1-1=0[/tex]
[tex]f(0)=2(0)+0-1=0+0-1=-1[/tex]
[tex]f(1)=2(1)^2+(1)-1 = 2+1-1=2[/tex]
The range is simply the set of all possible outputs.
