Not a function Function Not a function Relation 3 \[ \{(2,0),(2,-1),(2,-3),(2,2)\} \] Function Not a function Relation 4 \[ \{(z,-9),(m, 0),(u, 1),(j,-2)\} \] Function Not a function

1. **Definition of a Function** A relation is a function if and only if every input is associated with exactly one output. 2. **Analyzing Relation 3** The relation is \[ \{(2,0),\,(2,-1),\,(2,-3),\,(2,2)\}. \] - Here, the input \(2\) appears in every ordered pair, but it is associated with multiple different outputs: \(0\), \(-1\), \(-3\), and \(2\). - Since the same input \(2\) has more than one output, the relation does not satisfy the definition of a function. **Conclusion:** Relation 3 is **not a function**. 3. **Analyzing Relation 4** The relation is \[ \{(z,-9),\,(m,0),\,(u,1),\,(j,-2)\}. \] - Here, the first elements \(z\), \(m\), \(u\), and \(j\) serve as the inputs. - Provided that \(z\), \(m\), \(u\), and \(j\) are distinct (which is the normal assumption), each input is paired with exactly one output. **Conclusion:** Relation 4 is a **function**.