def sigmoid(x):
    """Sigmoid activation function"""
    return 1 / (1 + np.exp(-np.clip(x, -500, 500)))  # Clip to prevent overflow

# Test sigmoid on different inputs
test_values = np.array([-10, -1, 0, 1, 10])
sigmoid_values = sigmoid(test_values)

print("Sigmoid function behavior:")
for i, val in enumerate(test_values):
    print(f"  sigmoid({val:3.0f}) = {sigmoid_values[i]:.3f}")

# Visualize sigmoid
x_range = np.linspace(-10, 10, 100)
y_sigmoid = sigmoid(x_range)
plt.figure(figsize=(8, 4))
plt.plot(x_range, y_sigmoid, 'b-', linewidth=2)
plt.title('Sigmoid Activation Function')
plt.xlabel('x')
plt.ylabel('sigmoid(x)')
plt.grid(True, alpha=0.3)
plt.show()