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}

Answer:

B. ${y|y\geq - 2}$

Explanation:

Step1: Analyze absolute - value property

The absolute - value function $|a|=\begin{cases}a, & a\geq0\-a, & a < 0\end{cases}$, and $|a|\geq0$ for all real numbers $a$. 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 $g(x)=|x - 12|-2\geq0 - 2$. So $g(x)\geq - 2$. The range of the function $g(x)$ is the set of all $y$ such that $y\geq - 2$, which is written as ${y|y\geq - 2}$.