Question

1. on the set of axes below, graph the function $y = |x + 1|$

state the range of the function.
$y \geq 0$
state the domain over which the function is increasing.
$x > -1$

Explanation:

Step1: Choose x-values, compute y

Select $x = -3, -2, -1, 0, 1, 2$
For $x=-3$: $y=|-3+1|=|-2|=2$
For $x=-2$: $y=|-2+1|=|-1|=1$
For $x=-1$: $y=|-1+1|=|0|=0$
For $x=0$: $y=|0+1|=|1|=1$
For $x=1$: $y=|1+1|=|2|=2$
For $x=2$: $y=|2+1|=|3|=3$

Step2: Populate the table

Organize $(x,y)$ pairs into the table:

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

Answer:

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

(Note: The provided range $y\geq0$ and increasing domain $x>-1$ are already correct for the function $y=|x+1|$)