Defining a Step Function: Checking for Accuracy

[EvLer]

I just want to check if I got this right.
Given this graph, I need to define a step function:

         |
---------| C
         |
_________|_______________
         |
      -C |_________
         |

So, my definition is: C[-u(t) + u(-t)].
Thanks for checking this.

 

[Phymath]

f(x) = {c, x < 0}{-c, x > 0}, f(x) is undef at x = 0, though, |f(0)| = c

 

[EvLer]

Thanks for reply.

I understand the form of the function, but this is for an engineering class, so we have to express everything in terms of u(t), etc. So, this is what I need for some-one to double check.
And they actually never say that there is a discontinuity at 0, because we have to find values for t >=0 and so on.

 

[Townsend]

I don't think your definition will work so well. Let's say 0<c, and 0<t<c. What is the value of your function? well $$u_c(t)=0 \mbox{ for } t<c \mbox{ and } u_c(-t)=0 \mbox{ for } t<c$$ since t will just be negative it will still be less than c. So your function will not work in that case. I just worked from left to right to construct the definition and came up with
$$C[1-2u_c(t)]$$

Which seems to work for all t in R.

Regards