Question

Записать 5 линейных функций и построить одну из них

Answer 1

Ответ:

y=x

y=x+1

y=-x+2

y=-2x-2

y=-x

Объяснение:

y=-x

Answer 2

Linear Functions

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the general form of `y = mx + b`, where `m` is the slope of the line and `b` is the y-intercept.

Here are five examples of linear functions:

1. Function 1: - Equation: `y = 2x + 3` - This function has a slope of 2 and a y-intercept of 3.

2. Function 2: - Equation: `y = -0.5x + 1` - This function has a slope of -0.5 and a y-intercept of 1.

3. Function 3: - Equation: `y = 4x - 2` - This function has a slope of 4 and a y-intercept of -2.

4. Function 4: - Equation: `y = 0.75x + 0` - This function has a slope of 0.75 and a y-intercept of 0.

5. Function 5: - Equation: `y = -3x + 5` - This function has a slope of -3 and a y-intercept of 5.

Let's plot one of these functions, Function 1 (`y = 2x + 3`), as an example:

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-10, 10, 100)  # Generate 100 x-values from -10 to 10
y = 2 * x + 3  # Calculate corresponding y-values using the function y = 2x + 3

plt.plot(x, y)  # Plot the line
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of y = 2x + 3')
plt.grid(True)
plt.show()

The code above uses the `matplotlib` library in Python to plot the graph of the linear function `y = 2x + 3`. The x-values range from -10 to 10, and the corresponding y-values are calculated using the equation. The resulting line is then plotted on a graph.

Please note that the other four functions can be plotted in a similar manner by replacing the equation and the corresponding values of `m` and `b`.

I hope this helps! Let me know if you have any further questions.