Question

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

Explanation:

Step1: Recall absolute value property

The absolute value function \(|a|\) has a range of \(a \geq 0\) for all real numbers \(a\). For \(g(x)=|x - 12|-2\), let \(a=x - 12\), so \(|x - 12|\geq0\).

Step2: Analyze the range of \(g(x)\)

Since \(|x - 12|\geq0\), we can add \(-2\) to both sides of the inequality. So \(|x - 12|-2\geq0 - 2\), which simplifies to \(g(x)\geq - 2\). This means the range of \(g(x)\) is all real numbers \(y\) such that \(y\geq - 2\), or \(\{y|y\geq - 2\}\).

Answer:

\(\{y|y\geq - 2\}\) (corresponding to the option: \(\boldsymbol{\{y|y\geq - 2\}}\))