(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

To solve the problem step by step, we will break it down into parts (a), (b), and (c) as specified.

### Part (a): Draw the graph of \( f(x) \)

1. **Define the function**:
The function \( f(x) \) is defined piecewise as follows:
- \( f(x) = 1 \) for \( |x| \geq 1 \)
- \( f(x) = \frac{1}{n^2} \) for \( \frac{1}{n} < |x| < \frac{1}{n-1} \) where \( n = 2, 3, \ldots \)
...