Question

In Problems 40 – 54 match the given graph with one of the functions in (a)-(f). The graph $f\left(t\right)$ is given is Figure 7.3.11

$$\begin{gathered} a.f\left(t\right)-f\left(t\right)u(t-a) \\ b.f(t-b)u(t-b) \\ c.f\left(t\right)u(t-a) \\ d.f\left(t\right)-f\left(t\right)u(t-b) \\ e.f\left(t\right)u(t-a)-f\left(t\right)u(t-b) \\ f.f(t-a)u(t-a)-f(t-a)u(t-b) \end{gathered}$$

Figure graph for problem 50

Short answer

The given graph matches with 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.

$$\begin{gathered} u(t-a)=\left\{0,0\le 1<a\right\} \\ u(t-a)=\left\{1t>a\right\} \end{gathered}$$

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.