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.

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

Figure graph for problem 53

Short answer

The given graph matches the function (a)$f\left(t\right)-f\left(t\right)u(t-a)$

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

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

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