Question

make a table of values for the following equation. then graph the equation.
$y = |x| + 1$
complete the table of values below.

x	y
-3	\square
-1	\square
0	\square
1	\square
3	\square

(simplify your answers.)

Explanation:

Step1: Substitute \( x = -3 \) into \( y = |x| + 1 \)

The absolute value of \( -3 \) is \( |-3| = 3 \), so \( y = 3 + 1 = 4 \).

Step2: Substitute \( x = -1 \) into \( y = |x| + 1 \)

The absolute value of \( -1 \) is \( |-1| = 1 \), so \( y = 1 + 1 = 2 \).

Step3: Substitute \( x = 0 \) into \( y = |x| + 1 \)

The absolute value of \( 0 \) is \( |0| = 0 \), so \( y = 0 + 1 = 1 \).

Step4: Substitute \( x = 1 \) into \( y = |x| + 1 \)

The absolute value of \( 1 \) is \( |1| = 1 \), so \( y = 1 + 1 = 2 \).

Step5: Substitute \( x = 3 \) into \( y = |x| + 1 \)

The absolute value of \( 3 \) is \( |3| = 3 \), so \( y = 3 + 1 = 4 \).

Answer:

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

The completed table is:

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