Answer
(a) The graph is as shown.
(b) The $x$-intercepts are $(-1,0)$ and $(5,0)$.
(c) The solution is: $x=-1,5$
(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 $(-1,0)$ and $(5,0)$.
(c) Setting $y=0$:
$$0=|x-2|-3$$
$$|x-2|=3$$
Taking the positive:
$$x-2=3$$
$$x=5$$
Taking the negative:
$$x-2=-3$$
$$x=-1$$
Thus, the solution is:
$$x=-1,5$$
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
