Finding the function f(t) from it's graph

Question

enter image description here

Here's what I have so far:

$$f(t) = (-2(t+1)+1.5) \times (u(t+1)-u(t)) + (t-0.5) \times (u(t)-u(t-1)) + 0.5\cos(\pi t) \times (u(t-1)-u(t-3))$$

I found the majority of this function, but I'm not sure how to account for the edges (the vertical lines at \$t=-1\$ and \$t = 3\$).

Because I haven't accounted for the vertical lines at t=-1 and t=3. — 01001000 01101001, Jun 17 '15 at 02:01
I'm voting to close this question as off-topic because it's a general math problem. — PeterJ, Jun 20 '15 at 10:29

score 2 · Accepted Answer · answered Jun 17 '15 at 02:07

The Heaviside function has a discontinuity at \$t = 0\$, so your terms that look like $$ u(t) - u(t + 1) $$ already deal with the discontinuities at \$t = -1, 3\$. I've added a picture of the first term to show the jump at \$-1\$.

enter image description here

Note that some plotting software doesn't show these discontinuities as vertical lines. This makes sense, because the function can only have one value for any given \$t\$ - a vertical line doesn't pass the vertical line test.

+1 for "a vertical line doesn't pass the vertical line test", — Carsten S, Jun 23 '15 at 17:52

Finding the function f(t) from it's graph

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