(a) Draw the graph of `f(x) = ={{:(1",",, |x| ge 1), ((1)/(n^(2)) ",",, (1)/(n)lt |x|lt (1)/(n-1)","n= 2"," 3"," ...), (0",",, x=0):}`
(b) Sketch the region `y le -1`.
(c) Sketch the region `|x| lt 3`.

Explanation

(a) `f(x) = ={{:(1",",, |x| ge 1), ((1)/(n^(2)) ",",, (1)/(n)lt |x|lt (1)/(n-1)","n= 2"," 3"," ...), (0",",, x=0):}`
`" "={{:(1",",, xle -1 or x ge 1), ((1)/(4) ",",, x in (-1, -(1)/(2))uu ((1)/(2), 1)), ((1)/(9) ",",, x in ((-1)/(2), (-1)/(3))uu ((1)/(3), (1)/(2))),(...,,):}`

(b) `y le -1`
For `y le -1`, first draw the line `y =-1`. All the points satisfying `y le -1` have ordinate greater than, or equal to, -1, i.e. all the points lying on or below the line `y=-1`.
The region is as shown in the following region.

(c ) ` |x| lt 3`
So `-3 lt x lt 3`, i.e. all points have abscissae lying between -3 and 3. Hence all the points lying between the lines `x=-3 and x=3`.