Sharktooth Functions in 1-dimension

import numpy as np 
import matplotlib.pyplot as plt

def max_conv_operator(samples, f_samples, input, L):
    return np.max(f_samples - L * np.abs(input - samples))

def sharktooth_function(function, x_start, x_stop, number_of_sharkteeth, L, plot_arg):
    samples = np.random.uniform(x_start,x_stop, number_of_sharkteeth)
    f_samples = function(samples)
    x = np.linspace(x_start, x_stop, 10000)
    approximate_y = []
    for i in range(len(x)):
        approximate_y.append(max_conv_operator(samples, f_samples, x[i], L))
    error = np.max(np.abs(f(x) - approximate_y))
    if plot_arg == 1:
        plt.plot(x,approximate_y)
    else:
        return error

def f(x):
    return x/(x+2)

L = [1,4,8,16]
plt.figure(figsize=(17,5))
for L in L:
    errors = []
    for i in range(1,50):
        errors.append(sharktooth_function(f,0,1,i,L,0))
    import matplotlib.pyplot as plt
    plt.plot(errors, label =L)

plt.xlabel("Number of teeth")
plt.ylabel(r"$\sup_{x\in x_i} | f(x)- \mathfrak{R}_{\mathfrak{r}} ( \mathsf{P})|$")
plt.legend()
plt.title("Sup of deviance from  f(x) as the number of teeth increase and as we get closer to L")

Text(0.5, 1.0, 'Sup of deviance from  f(x) as the number of teeth increase and as we get closer to L')