as np import matplotlib.pyplot as plt

Define the function y = |(x - 1) / (x + 1)|

def func(x): return np.abs((x - 1) / (x + 1))

Generate x values, avoiding x = -1 to prevent division by zero

x = np.linspace(-10, 10, 1000) x = x[x != -1]

Calculate y values

y = func(x)

Plot the function

plt.figure(figsize=(8, 6)) plt.plot(x, y, label="y = |(x - 1) / (x + 1)|") plt.axhline(0, color='black', linewidth=0.8, linestyle='--') # x-axis plt.axvline(0, color='black', linewidth=0.8, linestyle='--') # y-axis plt.title("Graph of y = |(x - 1) / (x + 1)|") plt.xlabel("x") plt.ylabel("y") plt.ylim(0, 10) # Set y-axis limits for clarity plt.legend() pltHere is the graph of the function $y = \left| \frac{x - 1}{x + 1} \right|$. Let me know if you'd like an explanation of the features of the graph or any related queries.

Here are five related questions to deepen your understanding:

1. What happens to the function as $x$ approaches -1?
2. How does the graph change if the absolute value is removed?
3. What are the domain and range of this function?
4. How would the graph be affected if the numerator was $x+1$ instead of $x-1$?
5. Can this function be integrated over a specified interval? If so, how?

Tip: Pay attention to critical points like where the function is undefined or changes rapidly; these are often key to