The range is the set of values of #f(x)# you can get from your domain. So given #f(x)=x^2-1# and domain #D={-2,-1,0,2}#, all you have to do is plug in the elements of your domain into your function.
#color(red)(x=-2)#
#[1]" "f(-2)=(-2)^2-1#
#[2]" "f(-2)=4-1#
#[3]" "color(red)(f(-2)=3)#
#color(blue)(x=-1)#
#[1]" "f(-1)=(-1)^2-1#
#[2]" "f(-1)=1-1#
#[3]" "color(blue)(f(-1)=0)#
#color(green)(x=0)#
#[1]" "f(0)=(0)^2-1#
#[2]" "f(0)=0-1#
#[3]" "color(green)(f(0)=-1)#
#color(orange)(x=2)#
#[1]" "f(2)=(2)^2-1#
#[2]" "f(2)=4-1#
#[3]" "color(orange)(f(2)=3)#
Now that you have solved for all the possible values of #f(x)#, your range is:
#R={-1,0,3}#
