import numpy as np
import matplotlib.pyplot as plt

Define the function f(x)

def f(x):
return 1/(x**2 - 1)

Generate x values

x = np.linspace(-5, 5, 1000)

Calculate y values

y = f(x)

Create the plot

plt.figure(figsize=(10,6))
plt.plot(x, y, label='f(x)=1/(x^2-1)')
plt.axvline(x=1, color='r', linestyle='--', label='Vertical asymptote at x=1')
plt.axvline(x=-1, color='y', linestyle='--', label='Vertical asymptote at x=-1')
plt.xlabel('x')
plt.ylabel('f(x)')
plt.title('Graph of f(x)=1/(x^2-1)')
plt.legend()
plt.grid(True)
plt.show()