Which relation from (A={1,2,3}) to (B={2,3,4,5,6}) represents (f(x)=x+2)?

Correct answer: \({(1,3),(2,4),(3,5)})

The direct answer is A: the relation is \(\{(1,3),(2,4),(3,5)\}\). A function rule tells us to take each input from the domain and calculate exactly one output. Here \(f(x)=x+2\). Step by step, \(f(1)=1+2=3\), \(f(2)=2+2=4\), and \(f(3)=3+2=5\). All outputs belong to \(B\), so this is a valid relation from \(A\) to \(B\). Option A is correct because it contains precisely these three ordered pairs. Option B uses \(x+1\), since it gives 2, 3, and 4. Option C reverses the direction of the pairs and does not have the required domain elements as first entries. Option D gives 4, 5, and 6, which corresponds to \(x+3\), not \(x+2\). Remember: substitute every domain value into the formula, and write the input first and its image second.