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Sketch x[n] built from unit steps

Short answer

x[n] = 1 for −2 ≤ n ≤ 2, equals n for 3 ≤ n ≤ 5, and 0 elsewhere. The discrete-time plot consists of samples: (−2,1), (−1,1), (0,1), (1,1), (2,1), (3,3), (4,4), (5,5).

Draw the following signal x[n] = u[n+2] − u[n−3] + nu[n−3] − nu[n−6].

Evaluate each term range by range:

  • u[n+2]−u[n−3]u[n+2] - u[n-3] = 1 for −2≤n≤2-2 \le n \le 2, else 0.
  • nu[n−3]−nu[n−6]=n (u[n−3]−u[n−6])n u[n-3] - n u[n-6] = n\,(u[n-3]-u[n-6]) = nn for 3≤n≤53 \le n \le 5, else 0.
nn≤ −3−2−1012345≥ 6
x[n]x[n]0111113450

So x[n]={1,1,1‾,1,1,3,4,5}x[n] = \{1, 1, \underline{1}, 1, 1, 3, 4, 5\} for n=−2n = -2 to 55 (underline marks n=0n = 0).

 x[n]
  5 |                          o
  4 |                       o  |
  3 |                    o  |  |
  2 |                    |  |  |
  1 |     o  o  o  o  o  |  |  |
    |     |  |  |  |  |  |  |  |
 ---+--+--+--+--+--+--+--+--+--+--+--> n
      -3 -2 -1  0  1  2  3  4  5  6

✓ Answer checked by Claude Opus 5.5 (high effort)

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