What is the range of the graph of the function \(y=|x-1|+|x+1|\)?

Correct answer: \([2,\infty)\)

The function represents the sum of the distances of \(x\) from 1 and from \(-1\). By the triangle inequality, \(|x-1|+|x+1|\geq |(x-1)-(x+1)|=2\). For \(-1\leq x\leq 1\), this sum is exactly 2, and outside this interval it increases above 2. Hence the range is \([2,\infty)\). Option B incorrectly assumes that the minimum can be 0, although the two points are 2 units apart. Exam tip: For a sum of absolute-value terms, check the interval between their critical points to find the minimum.