Answer
(a) The graph is as shown.
(b) The $x$-intercepts are $(-3,0)$ and $(1,0)$.
(c) The solution is: $x=-3,1$
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
Work Step by Step
(a) The graph is as shown.
(b) The $x$-intercepts are $(-3,0)$ and $(1,0)$.
(c) Setting $y=0$:
$$0=|x+1|-2$$
$$|x+1|=2$$
Taking the positive:
$$x+1=2$$
$$x=1$$
Taking the negative:
$$x+1=-2$$
$$x=-3$$
Thus, the solution is:
$$x=-3,1$$
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
