Question

x | x - 3 | y = |x - 3|
0 | -3 | blank
1 | -2 | blank
2 | -1 | blank
3 | 0 | blank
4 | 1 | blank
5 | 2 | blank

Explanation:

Step1: Recall absolute value definition

The absolute value of a number \( a \), denoted \( |a| \), is \( a \) if \( a \geq 0 \) and \( -a \) if \( a < 0 \).

Step2: Calculate for \( x = 0 \)

For \( x = 0 \), \( x - 3=-3 \). Since \( -3 < 0 \), \( |-3| = -(-3)=3 \).

Step3: Calculate for \( x = 1 \)

For \( x = 1 \), \( x - 3=-2 \). Since \( -2 < 0 \), \( |-2| = -(-2)=2 \).

Step4: Calculate for \( x = 2 \)

For \( x = 2 \), \( x - 3=-1 \). Since \( -1 < 0 \), \( |-1| = -(-1)=1 \).

Step5: Calculate for \( x = 3 \)

For \( x = 3 \), \( x - 3 = 0 \). So \( |0| = 0 \).

Step6: Calculate for \( x = 4 \)

For \( x = 4 \), \( x - 3 = 1 \). Since \( 1\geq0 \), \( |1| = 1 \).

Step7: Calculate for \( x = 5 \)

For \( x = 5 \), \( x - 3 = 2 \). Since \( 2\geq0 \), \( |2| = 2 \).

Answer:

For \( x = 0 \), \( y = 3 \); for \( x = 1 \), \( y = 2 \); for \( x = 2 \), \( y = 1 \); for \( x = 3 \), \( y = 0 \); for \( x = 4 \), \( y = 1 \); for \( x = 5 \), \( y = 2 \)

Filling the table:

\( x \)	\( x - 3 \)	\( y =	x - 3	\)
1	-2	2
2	-1	1
3	0	0
4	1	1
5	2	2