If \(f:\{0,1,2,3,4\}\to\{0,1,2,3,4\}\) is defined by the remainder obtained when \(3x\) is divided by \(5\), what is the range of \(f\)?

Correct answer: \(\{0,1,2,3,4\}\)

Substituting \(x=0,1,2,3,4\) gives the remainders \(0,3,1,4,2\), respectively. Hence the set of attained values is \(\{0,1,2,3,4\}\), so option A is correct. Option D includes only some even remainders and omits \(1\) and \(3\). Exam tip: To find the range, evaluate the function for every element of the domain; do not simply copy the codomain.