**π‘ Problem Formulation:** We are tasked with plotting the mathematical function y = 1/x. It’s a common equation representing a hyperbola. Python users often require to visualize such functions for analysis and presentation purposes. The input to our plotting methods will be a range of ‘x’ values, while the output will be a plot of the corresponding ‘y’ values that form the graph of y = 1/x.

## Method 1: Using matplotlib.pyplot

Matplotlib is a comprehensive library for creating static, animated, and interactive plots in Python. The `matplotlib.pyplot`

module provides a MATLAB-like interface for plotting. Users can plot a wide range of graphs, including y = 1/x, by defining the range of x-values and using the `plot()`

function to render the graph.

Here’s an example:

import matplotlib.pyplot as plt import numpy as np x = np.linspace(0.1, 10, 100) # Avoid zero to prevent division by zero y = 1 / x plt.plot(x, y) plt.xlabel('x') plt.ylabel('y') plt.title('Plot of y = 1/x') plt.show()

The output is a plot displaying the hyperbolic curve of y = 1/x.

This code snippet creates a range of x-values between 0.1 and 10, avoiding zero to prevent division by zero errors. It calculates the corresponding y-values by applying the function 1/x. Matplotlib’s `plot()`

function is used to generate and display the plot with labeled axes and a title.

## Method 2: Using seaborn.lineplot

Seaborn is a data visualization library based on matplotlib that provides a high-level interface for drawing attractive and informative statistical graphics. The `seaborn.lineplot`

function is a specialized version for creating line plots, perfect for plotting mathematical functions like y = 1/x with enhanced aesthetics.

Here’s an example:

import seaborn as sns import numpy as np x = np.linspace(0.1, 10, 100) y = 1 / x sns.lineplot(x, y) sns.set_theme() plt.xlabel('x') plt.ylabel('y') plt.title('Seaborn plot of y = 1/x') plt.show()

The output is a Seaborn-styled line plot of the function y = 1/x.

This code snippet uses Seaborn’s `lineplot()`

function for plotting, which automatically styles the plot with Seaborn’s default theme. The x and y axes are labeled, and a title is added for clarity. The plot represents the inverse relationship between x and y.

## Method 3: Using pandas and matplotlib

Pandas is a data analysis and manipulation library, which, when combined with matplotlib, can be used for effective data plotting. By creating a DataFrame that maps ‘x’ to ‘y’, one can plot the DataFrame using the `plot()`

method directly.

Here’s an example:

import pandas as pd import matplotlib.pyplot as plt x = pd.Series(np.linspace(0.1, 10, 100)) y = 1 / x df = pd.DataFrame({'x': x, 'y': y}) df.plot('x', 'y', legend=False) plt.xlabel('x') plt.ylabel('y') plt.title('Pandas plot of y = 1/x') plt.show()

The output is a matplotlib plot produced directly from a pandas DataFrame of y = 1/x.

In this method, a pandas DataFrame is created using a Series of x-values and their corresponding y-values. The DataFrame’s `plot()`

method is then called, specifying the columns to use for the x and y axes. Pandas automatically uses matplotlib for plotting, so customization options are similar to Method 1.

## Method 4: Using Plotly

Plotly’s Python graphing library makes interactive, publication-quality graphs online. One can easily create a plot of y = 1/x using Plotly’s express module, which offers a simple syntax for complex charts.

Here’s an example:

import plotly.express as px import numpy as np x = np.linspace(0.1, 10, 100) y = 1 / x fig = px.line(x=x, y=y, labels={'x':'x', 'y':'y'}, title='Plotly plot of y = 1/x') fig.show()

The output is an interactive Plotly line plot of y = 1/x.

This example utilizes Plotly Express to create an interactive line plot. The user can hover over the plot to see the exact values at different points. This method greatly enhances user engagement and is an excellent choice for web-based data presentations.

## Bonus One-Liner Method 5: Using pyplot’s plot function in one line

For a quick and straightforward approach, one can use matplotlib’s `plt.plot()`

function to create a plot of y = 1/x in a single line of code. This method is recommended for fast prototyping or when plot customizations are not necessary.

Here’s an example:

plt.plot(np.linspace(0.1, 10, 100), 1 / np.linspace(0.1, 10, 100)); plt.show()

The output is a simple matplotlib plot of y = 1/x.

This compact one-liner generates a range of x-values, calculates the corresponding y-values, and plots the graph, all using matplotlib. It’s extremely concise but offers less customization and clarity than the other methods.

## Summary/Discussion

**Method 1: Matplotlib.pyplot.**Strengths: Widely used, great for detailed customizations. Weaknesses: Static plots.**Method 2: Seaborn.lineplot.**Strengths: Aesthetically pleasing defaults, good for statistical data. Weaknesses: Less control than pure matplotlib.**Method 3: Pandas and matplotlib.**Strengths: Uses the familiar pandas interface, great for data-frames. Weaknesses: Requires additional memory for pandas data structures.**Method 4: Plotly.**Strengths: Interactive, user-friendly, and web-friendly plots. Weaknesses: May have a steeper learning curve for some users.**Method 5: One-liner matplotlib.**Strengths: Fast and concise for quick checks. Weaknesses: Very limited customization and functionality.