what is the range of the function g(x) = |x - 12| - 2?\n{y | y > -2}\n{y | y ≥ -2}\n{y | y > 12}\n{y | y ≥ 12}

Explanation:

Step1: Recall property of absolute - value

The absolute - value function (|a|\geq0) for any real number (a). In the function (g(x)=|x - 12|-2), let (a=x - 12). Then (|x - 12|\geq0).

Step2: Find the range of (g(x))

If (|x - 12|\geq0), then (|x - 12|-2\geq0 - 2). So (g(x)=|x - 12|-2\geq - 2).

Answer:

({y|y\geq - 2})