import numpy as np import matplotlib.pyplot as plt

Define the unit step function

def u(t): return np.where(t < 0, 0, 1)

Define the function x(t)

def x(t): return 0.5*(np.exp(-2t) - np.exp(-4t))u(t) - 0.5(np.exp(-2t+6) - np.exp(-4t+12))*u(t-3)

Generate the time vector

t = np.linspace(0, 10, 1000)

Generate the function values

y = x(t)

Plot the function

plt.plot(t, y, '-k', linewidth=2)

Add title and axis labels

plt.title('Plot of x(t)') plt.xlabel('t') plt.ylabel('x(t)')

Add grid lines

plt.grid(True)

Show the plot

plt.show()