Question

y = -|x + 1|
column by column

x	x + 1		x + 1		y = -	x + 1
-4
-3
-2
-1
0
1
2

Explanation:

Step1: Calculate $x + 1$ for $x=-4$

$-4 + 1=-3$

Step2: Calculate $|x + 1|$ for $x=-4$

$| - 4+1|=|-3| = 3$

Step3: Calculate $y=-|x + 1|$ for $x=-4$

$y=-| - 4 + 1|=-3$

For the row where $x = - 4$:
The first blank (value of $x + 1$) is $-3$, the second blank (value of $|x + 1|$) is $3$, and the third blank (value of $y=-|x + 1|$) is $-3$.

We can continue this process for other values of $x$:
When $x=-3$:

Step1: Calculate $x + 1$

$-3 + 1=-2$

Step2: Calculate $|x + 1|$

$| - 3+1|=|-2| = 2$

Step3: Calculate $y=-|x + 1|$

$y=-| - 3 + 1|=-2$

When $x=-2$:

Step1: Calculate $x + 1$

$-2+1=-1$

Step2: Calculate $|x + 1|$

$| - 2 + 1|=|-1|=1$

Step3: Calculate $y=-|x + 1|$

$y=-| - 2+1|=-1$

When $x=-1$:

Step1: Calculate $x + 1$

$-1 + 1=0$

Step2: Calculate $|x + 1|$

$| - 1+1|=|0| = 0$

Step3: Calculate $y=-|x + 1|$

$y=-| - 1 + 1|=0$

When $x = 0$:

Step1: Calculate $x + 1$

$0+1=1$

Step2: Calculate $|x + 1|$

$|0 + 1|=|1| = 1$

Step3: Calculate $y=-|x + 1|$

$y=-|0 + 1|=-1$

When $x = 1$:

Step1: Calculate $x + 1$

$1+1=2$

Step2: Calculate $|x + 1|$

$|1 + 1|=|2| = 2$

Step3: Calculate $y=-|x + 1|$

$y=-|1 + 1|=-2$

When $x = 2$:

Step1: Calculate $x + 1$

$2+1=3$

Step2: Calculate $|x + 1|$

$|2 + 1|=|3| = 3$

Step3: Calculate $y=-|x + 1|$

$y=-|2 + 1|=-3$

The completed table:

$x$	$x + 1$	$	x + 1	$	$y=-	x + 1	$
$-3$	$-2$	$2$	$-2$
$-2$	$-1$	$1$	$-1$
$-1$	$0$	$0$	$0$
$0$	$1$	$1$	$-1$
$1$	$2$	$2$	$-2$
$2$	$3$	$3$	$-3$

Answer:

$x$	$x + 1$	$	x + 1	$	$y=-	x + 1	$
$-3$	$-2$	$2$	$-2$
$-2$	$-1$	$1$	$-1$
$-1$	$0$	$0$	$0$
$0$	$1$	$1$	$-1$
$1$	$2$	$2$	$-2$
$2$	$3$	$3$	$-3$