text: # Machine Learning/Data Science Precourse Work
  
  # ###
  # LAMBDA SCHOOL
  # ###
  # MIT LICENSE
  # ###
  
  # Free example function definition
  # This function passes one of the 11 tests contained inside of test.py. Write the rest, defined in README.md, here,
  # and execute python test.py to test. Passing this precourse work will greatly increase your odds of acceptance
  # into the program.
  import math
  import numpy as np
  
  
  def f(x):
      return x**2
  
  
  def f_2(x):
      return x**3
  
  
  def f_3(x):
      return (x**3) + (5*x)
  
  
  def d_f(x):
      return 2*x
  
  
  def d_f_2(x):
      return 3*(x**2)
  
  
  def d_f_3(x):
      return 3*(x**2) + 5
  
  
  # for all values of x, return x + y
  def vector_sum(x, y):
      for num in range(len(x)):
          return [x[num] + y[num]]
  
  
  #  for all values of x, return x - y
  def vector_less(x, y):
      for num in range(len(x)):
          return [x[num] - y[num]]
  
  
  def vector_magnitude(v):
      sqvector = 0
      for vector in v:
          sqvector += vector**2
      return math.sqrt(sqvector)
  
  
  def vec5():
      return np.array([1, 1, 1, 1, 1])
  
  
  def vec3():
      return np.array([0, 0, 0])
  
  
  def vec2_1():
      return np.array([1, 0])
  
  
  def vec2_2():
      return np.array([0, 1])
  
  
  def matrix_multiply(vec, matrix):
      return np.dot(vec, matrix)
  