import numpy as np
import matplotlib.pyplot as plt

def u(x, p):
    if p == 0:
        return x
    else:
        return (np.exp(p*x)-1)/(np.exp(p)-1)


x = np.linspace(0, 1, 200)

p_values = [-10, -2, 0, 2, 10]
colors = ['purple', 'blue', 'black', 'orange', 'red']



plt.figure(figsize=(7,5))
for p, c in zip(p_values, colors):
    plt.plot(x, u(x, p), label=f"p = {p}", color=c, linewidth=2)


plt.xlabel("x")
plt.ylabel("u(x)")
plt.legend()
plt.grid(True)
plt.show()