Question

given the function below, fill in the table of values, use the table of values to graph the function, and then identify the function’s domain and range.
$y = |x| - 3$
(table with columns x, |x|, $y = |x| - 3$; rows: -3 with |x|=3, y=0; -2 with empty |x| and y; -1 with empty |x| and y)

Explanation:

Step1: Calculate |x| for x = -2

The absolute value of a number is its distance from 0 on the number line, so \(|-2| = 2\).

Step2: Calculate y = |x| - 3 for x = -2

Substitute |x| = 2 into the equation: \(y = 2 - 3 = -1\).

Answer:

For \(x = -2\), \(|x| = 2\) and \(y = |x| - 3 = -1\). So the filled table cells for \(x = -2\) are \(|x| = 2\) and \(y = -1\).