What is the range of that function?

The range is simply the set of possible outputs of a relation or function, which in this case is represented by the set of values in the oval on the right.
The input 1 maps to the output 2
The input 2 maps to the output 4
The input 3 maps to the output 9
The input 4 maps to the output 16
note: the domain would be {1,2,3,4} which is the set of input values shown in the oval on the left. It is the set of all possible inputs of a relation or function.