How do we plot $u(4−t)$, where $u(t)$ is a step function?

Question

How do we plot $u(4−t)$?

$u(t)$ is a step function:

$$u(t)=\begin{cases} 1&\text{ for }t \ge 0,\\ 0 & \text{ for }t \lt 0.\end{cases}$$

Answer 1

$u(4-t) = 1$ for $4-t\ge0$ so for $t\le4$

$u(4-t) = 0$ for $4-t\lt0$ so for $t\gt4$

Here is the plot:

Answer 2

Here's the trick:

$u(x)$ will evaluate to 1 if $x$ is positive and zero otherwise, whatever be the expression you have in the place of x.

So, for $u(4-t)$, we need to see what values of $t$ keep $(4-t)$ positive...

Answer 3

The unit step function has a single transition when the argument is zero.

Check where (4 - t) is zero, that's where the function switches from 0 to 1 or from 1 to 0. To know which transition it is, try a value for t less than or greater than 4, for instance t = 0.