import numpy as np
import matplotlib.pyplot as plt

plt.rcParams['text.usetex'] = True

# x = np.linspace(0, 2 * np.pi, 100)
x = np.arange(-2, 2, 0.1)

f = np.exp(-x**2)
g = np.sin(x**2)
h = np.sin(1 / (x**3 + 9))

plt.plot(x, f, "purple", label=r"$f(x) = \exp(-x^2)$")
plt.plot(x, g, "red", label=r"$g(x) = \sin(x^2)$")
plt.plot(x, h, "green", label=r"$h(x) = \frac{1}{x^3 + 9}$")

plt.title("A2.b)")
plt.xlabel("x")
plt.ylabel("y")
plt.legend()

plt.show()