If \(f:\{1,2,3,4,5\}\to\{1,2,3\}\) is defined by \(f(x)=\max(1,4-x)\), what is its range?

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

For the domain values, the function gives \(f(1)=3\), \(f(2)=2\), \(f(3)=1\), \(f(4)=1\), and \(f(5)=1\). Thus, the set of distinct output values, or the range, is \(\{1,2,3\}\). Option D includes only the repeated output 1 and omits 2 and 3. Exam tip: the range is the set of actual outputs, whereas the codomain may contain values that are not attained.