Question

describe the domain and range of $g(x)=|x|-2$
domain:
range:
$x\geq -2$ $y\geq -2$ $x\geq 0$ $y\geq 0$ $x\geq 2$ $y\geq 2$ all real numbers

Explanation:

Step1: Analyze the domain of \( g(x) = |x| - 2 \)

The absolute value function \( |x| \) is defined for all real numbers \( x \). Subtracting 2 from \( |x| \) does not restrict the values of \( x \) that we can input. So, the domain (all possible \( x \)-values) is all real numbers.

Step2: Analyze the range of \( g(x) = |x| - 2 \)

The absolute value \( |x| \) has a range of \( y \geq 0 \) (since the absolute value of any real number is non - negative). When we subtract 2 from \( |x| \), we shift the graph of \( |x| \) down by 2 units. So, the range of \( g(x)=|x|-2 \) is \( y\geq - 2 \).

Answer:

domain: all real numbers
range: \( y\geq - 2 \)