If (A={1,2,3}), (B={1,2,3,4}), and (f(x)=x+1), which statement about (f) is correct?

Correct answer: It is a function from (A) to (B) and range is ({2,3,4})

The direct answer is A: it is a function from \(A\) to \(B\), and its range is \(\{2,3,4\}\). Evaluate the rule for every domain element: \(f(1)=1+1=2\), \(f(2)=2+1=3\), and \(f(3)=3+1=4\). These outputs all lie in \(B=\{1,2,3,4\}\), so the mapping is a valid function. The outputs actually reached form the range, namely \(\{2,3,4\}\); the value 1 is in the codomain but is not reached. Option A is therefore correct. Option B is wrong because a function need not use every codomain element. Option C is wrong because obtaining 4 from input 3 is allowed; 4 belongs to B. Option D is wrong because it confuses codomain with range and includes 1, which is never an output. The range can be a proper subset of the codomain. Exam cue: calculate all images, check that they lie in the codomain, then list only the images actually obtained.