If (f={(1,4),(2,4),(3,5),(4,6)}), what is the range of (f)?

Correct answer: ({4,5,6})

The direct answer is C: {4,5,6}. The range of a function is the set of distinct output values, meaning the second components of its ordered pairs. The given pairs are (1,4), (2,4), (3,5), and (4,6). Their outputs are 4, 4, 5, and 6. A set does not repeat an element, so the repeated 4 is written only once. Hence the range is {4,5,6}. Option A, {1,2,3,4}, lists the input values, so it is the domain, not the range. Option B, {4,4,5,6}, lists the outputs but repeats 4; it is not written as a proper set of distinct elements. Option C correctly gives the distinct outputs. Option D, {1,4,5,6}, mixes an input value, 1, with output values and therefore does not represent the range. Notice that 4 appears as both an output and an input in different roles, but its role in the range is determined by its position as a second component. Memory cue: domain means first coordinates; range means distinct second coordinates actually obtained.