Question 709490
"Range" is what values the function is, what the set of function values is.  


Your example was specified to use x only between -1 and 0, inclusive.  If you SQUARE x, the result will be POSITIVE.  The domain values were specified as mostly negative, but any real number squared is POSITIVE.  


"what it means to say that the range is y ∈[0,1)",
The values for y are elements of the set of real numbers greater than or equal to zero, and less than 1.   Again, those are positive values (except for maybe zero) because f(x)=x^2 is positive.