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import numpy as np
import matplotlib.pyplot as plt

# Define the function
def q(x):
    return x / (x**2 + 36)

# Create an array of x values
x = np.linspace(-20, 20, 400)
y = q(x)

# Create the plot
plt.figure(figsize=(8, 6))
plt.plot(x, y, label=r'$q(x)=\frac{x}{x^2+36}$', color='blue')
plt.title('Graph of $q(x)=\\frac{x}{x^2+36}$')
plt.xlabel('x')
plt.ylabel('q(x)')
plt.axhline(0, color='black', linewidth=0.5)
plt.axvline(0, color='black', linewidth=0.5)
plt.legend()
plt.grid(True)
plt.show()