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I came across the following equation,

$f(t)=(1+2t)+(1-2t)u(t-1)+(3-2t)u(t-2)+(2t-5)u(t-3)$

Where $u(t-a)$ is a unit step (or Heaviside) function and it is defined as $u(t-a)=\begin{cases} 0&t<a\\1&t\geq a \end{cases}$

Now I have to plot $f(t)$ (in y-axis) vs $t$ (in x-axis). My confusion is in generating a expression for $f(t)$ in terms of $t$ alone by using appropriate expression for $u(t-1)$, $u(t-2)$, and $u(t-3)$. Can someone help me to get the correct plot?

Keerthi vasan
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  • you can do it using a different function for different intervals – Tortar Aug 19 '21 at 14:24
  • Are you plotting using any particular software? In GeoGebra, for example, you can define u(x) = If[x<0, 0, 1] then you can simply type f(x) as you have written it here. – Paul Aug 19 '21 at 14:44
  • @Paul I am interested in getting an expression for $f(t)$ in terms of $t$, where there will be a different expression for different intervals of $t$. – Keerthi vasan Aug 19 '21 at 14:48
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    Hint : when $t<1$ all three $u =0$ so $f(t) = 1+2t$, you are left with intervals $[1,2),[2,3),[3,\infty)$. – Tortar Aug 19 '21 at 15:59

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