How to plot x(t) = exp(-t)*u(t) using syms symbolic function?

I was asked to plot the function x(t) = exp(-t)*u(t) using symbolic matlab. However, I have been having trouble in creating the unit step function using the 'syms' function. I just wonder how can we set the bound for the value of t?

Attempt 1: trying to set the bound of syms t

syms t positive
syms u
%assume (t>0)
%u = inline('(t>=0)', 't')
x = sym('exp(t)*u')
x
x = subs(x,u,1)
ezplot(x);shg

I have tried to plot the exp(-t) and unit step(t) separately successfully; however, when I multiply them together, it gives me a graph will all zero value.

Attempt 2: trying to add 2 syms function together to create x(t)

   syms t u
   assume(t < 0)
   hold on;
   unit = heaviside(t)

   subplot(3,1,1);
   ezplot(unit)

   e = exp(t)
   subplot(3,1,2)
   ezplot(e)

   subplot(3,1,3)
   x = sym('exp(t)*u')
   ezplot(x);shg

Can someone please help me to point out how I should approach to this problem? I got stuck with this issue for hours and I still haven't been able to figure this out. Thanks!

Answer 1

[Mischa Kim]

Use the heaviside -function:

syms x
ezplot(heaviside(x)*exp(-x), [-2, 2])