Question

In Problems 40–54, match the given graph with one of the functions in (a)-(f). The graph is given as Figure 7.3.11.

1. $f\left(t\right)-f\left(t\right)u(t-a)$
   
2. $f(t-b)u(t-b)$
   
3. $f\left(t\right)u(t-a)$
   
4. $f\left(t\right)-f\left(t\right)u(t-b)$
   
5. $f\left(t\right)u(t-a)-f\left(t\right)u(t-b)$
   
6. $f(t-a)u(t-a)-f(t-a)u(t-b)$
   

Figure graph for problem 51

Short answer

The given graph matches the function (f).$f(t-a)u(t-a)-f(t-a)u(t-b)$

Step-by-step solution

Match the given and the original graph

Given:

Let us match the given graph to the original graph that is given below:

Unit function

Thus, the unit function $u(t-a)$is defined to b

$u(t-a)=\left\{\begin{array}{l}0\\ 1\end{array}\left.\begin{array}{r}0⩽1<a\\ t⩾a\end{array}\right\}\right.$

Thus, we conclude that (f) $f(t-a)u(t-a)-f(t-a)u(t-b)$is the function that matches the given graph.