If \(x\in\mathbb{R}\) and \(f(x)=2|x-6|-1\), what is the range of the function?

Correct answer: \([-1,\infty)\)

Since \(|x-6|\geq 0\), we have \(2|x-6|-1\geq -1\). At \(x=6\), \(|x-6|=0\), so \(f(6)=-1\), which is the minimum value. As \(|x-6|\) increases, the function increases without an upper bound. Therefore, the range is \([-1,\infty)\). Option B ignores the downward shift by 1. Exam tip: In \(a|x-h|+k\), if \(a>0\), the minimum value is \(k\).