Math for Data Science

Question

f(x) = 2x + 1

How to implement this formula in Python code?

Ushbu formulani Python kodida qanday amalga oshirish mumkin?

Answer 1

# Hi,
# Here's a more easy example:

# Define the function f(x)
def f(x):
return 2*x + 1

# Use list comprehension to generate f(x) values for a range of x values.
x_values = range(-10, 11) # Creates a range of x values from -10 to 10
f_values = [f(x) for x in x_values] # Calculate f(x) for each x using the function.

# Display the result
print(f"Input values: {list(x_values)}")
print(f"Function values: {f_values}")

# And here a more advanced one:

import matplotlib.pyplot as plt
import numpy as np

# Define the function f(x).
def f(x):
return 2*x + 1

# Generate x values as a range of numbers.
x = np.linspace(-10, 10, 100)

# Calculate corresponding y values using the function f(x).
y = f(x)

# Plot the graph.
plt.plot(x, y)
plt.title('Graph of f(x) = 2x + 1')
plt.xlabel('x')
plt.ylabel('f(x)')
plt.grid(True)

# Save the plot to a file.
plt.savefig('plot.png') # Saves the image as 'plot.png'

# Show the plot (this works locally and won't cause issues on SoloLearn)
plt.show() # Displays the plot

Answer 2

To implement this formula
𝑓(𝑥)=2𝑥+1 in Python, you can write a function that takes the value x and returns the result of f(x):
def f(x):
return 2 * x + 1

x = 5
result = f(x)
print(result)
This function f(x) calculates 2𝑥+1 for any value of x you provide.

Answer 3

def f(x):
return 2 * x + 1

x_values = [0, 1, 2, 3]
for x in x_values:
y = f(x)
print(y)

When dealing with real numbers, a subtle but important feature of functions is they often have an infinite number of x-values and resulting y-values. Ask yourself this: how many x-values can we put through the function y=2x+1? Rather than just 0, 1, 2, 3…why not 0, 0.5, 1, 1.5, 2, 2.5, 3 as shown in Table 1-2?

Answer 4

Sir kindly pls dont use such titles for simpler tasks 💀👍

Answer 5

HI, CodeStory ,

When working with functions like f(x) = 2x + 1 , in theory, you can input any real number (in R). However, in programming, real numbers are represented as floating-point numbers, which are only an approximation of the actual real numbers.

In fact, no matter how many decimal places a floating-point number has, it is still just an approximation of infinitely many real numbers that exist “out there” (in a philosophical sense).

This means that we can only compute the function for a limited set of values, not all real numbers. Using tools like numpy.linspace() (as shown in my earlier response), you can generate as many points as you need with the desired precision.

However, for a linear function like f(x) , you only need two points to fully understand its behavior. More points just give a finer representation.