Write f(x) = |x + 2| + |x - 3| without bars for (a) x < -2, (b) -2 ≤ x ≤ 3 and (c) x > 3.

$|x - a| < r$ means $a - r < x < a + r$. $[x]$ is the greatest integer not above $x$, and $\{x\} = x - [x]$ lies in $[0, 1)$. A piecewise function uses the rule for the piece that holds the input.