import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline

Power functions:

a = 4
b = -2
x = np.arange(1,1e5)
y = a*x**(b)

plt.plot(x,y,'-',lw=3)
plt.xlabel('x')
plt.ylabel('y')
plt.grid(True)

Exponential function

a = 4.0
b = -1.0
x = np.arange(1,100)
y = a**(b*x)

plt.plot(x,y,'-', lw=3)
plt.xlabel('x')
plt.ylabel('y')
plt.grid(True)

Log functions

a = 4.0
b = 1.0
x = np.arange(1,100)
y = a*np.log(b*x)

plt.plot(x,y,'-', lw=3)
plt.xlabel('x')
plt.ylabel('y')
plt.grid(True)