1. The problem states: Find the range of the relation $R_2 = \{(1,0),(2,2),(3,2),(4,2)\}$.\n\n2. The range of a relation is the set of all possible output values (second elements) from the ordered pairs.\n\n3. Looking at each ordered pair:\n- For $(1,0)$, the output is 0.\n- For $(2,2)$, the output is 2.\n- For $(3,2)$, the output is 2.\n- For $(4,2)$, the output is 2.\n\n4. Collecting all unique output values, the range is $\{0, 2\}$.\n\nFinal answer: The range of the relation is $\boxed{\{0, 2\}}$.