Question

Побудувати графік функції у= | 2/(х-1) |

Answer 1

Если достаточно только одного построения (без анализа), то вот таблица точек:

x y

-3.5 0.44

-3.0 0.5

-2.5 0.57

-2.0 0.67

-1.5 0.8

-1.0 1

-0.5 1.33

0 2

0.5 4

1.0 -

1.5 4

2.0 2

2.5 1.33

3.0 1

3.5 0.8

4.0 0.67

4.5 0.57

Answer 2

Graph of the Function y = |2/(x-1)|

To graph the function \( y = \left| \frac{2}{x-1} \right| \), we can use Python's Matplotlib library to visualize the function.

First, we need to define the range of x-values for the graph. Then, we can calculate the corresponding y-values using the function \( y = \left| \frac{2}{x-1} \right| \). Finally, we can plot the graph to visualize the function.

Here's a step-by-step guide to achieve this:

1. Define the Range of x-Values: We can choose a range of x-values to plot the graph. Let's say we want to plot the graph for x-values ranging from -10 to 10.

2. Calculate the Corresponding y-Values: Using the function \( y = \left| \frac{2}{x-1} \right| \), we can calculate the corresponding y-values for the chosen range of x-values.

3. Plot the Graph: After obtaining the x and y values, we can use Matplotlib to plot the graph of the function.

import matplotlib.pyplot as plt
import numpy as np

# Define the range of x-values
x = np.linspace(-10, 10, 400)  # 400 points between -10 and 10

# Calculate the corresponding y-values
y = np.abs(2 / (x - 1))

# Plot the graph
plt.plot(x, y, label=r'$y = \left| \frac{2}{x-1} \right|$', color='b')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of y = |2/(x-1)|')
plt.grid(True)
plt.show()

By running this code, we can visualize the graph of the function \( y = \left| \frac{2}{x-1} \right| \) over the specified range of x-values.

This approach allows us to see the behavior of the function and how it changes as x varies.