If \(A=\{1,2,3\}\) and \(B=\{0,1,2\}\), and \(f:A\to B\) is defined by \(f(x)\) being the remainder when \(x\) is divided by 2, what is the range of \(f\)?

Correct answer: \(\{0,1\}\)

For the elements of \(A\), we get \(f(1)=1\), \(f(2)=0\), and \(f(3)=1\). Thus, the only values actually obtained are 0 and 1, so the range of \(f\) is \(\{0,1\}\). Option C is the codomain \(B\), not the range, because 2 is not attained by the function. Exam tip: To find a range, evaluate the function for every element of the domain and list only the distinct outputs.