Question

Помогите с заданием, ну пожааааалуйста (уже три часа бьюсь с ним) Постройте график функций y = и y = -x+3 и укажите координаты точек пересечения.Заранее благодарю:3

Answer 1

Для того чтобы найти точки пересечения нужно их приравнять
$\frac{2}{x}=-x+3$ отсюда получим $x_{1}=1$
$x_{2}=2$ следовательно $y_{1}=2 y_{2}=1$ 

Answer 2

Plotting the Functions and Finding Intersection Points

To plot the functions y = x and y = -x + 3, we can create a graph and mark the points of intersection. Let's start by plotting the functions individually and then find their intersection points.

The first function, y = x, represents a straight line with a slope of 1 and passes through the origin (0,0). The second function, y = -x + 3, also represents a straight line but with a slope of -1 and intersects the y-axis at the point (0,3).

To find the intersection points, we need to solve the equations y = x and y = -x + 3 simultaneously. By substituting one equation into the other, we can find the x-coordinate of the intersection points. Then, by substituting the x-coordinate back into either equation, we can find the corresponding y-coordinate.

Let's solve the equations to find the coordinates of the intersection points.

Solving the Equations

Substituting y = x into y = -x + 3, we get:

x = -x + 3

Simplifying the equation, we have:

2x = 3

Dividing both sides by 2, we find:

x = 3/2

Substituting this value back into y = x, we get:

y = 3/2

Therefore, the coordinates of the intersection point are (3/2, 3/2).

Plotting the Graph

Now, let's plot the functions on a graph and mark the intersection point.

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-5, 5, 100)
y1 = x
y2 = -x + 3

plt.plot(x, y1, label='y = x')
plt.plot(x, y2, label='y = -x + 3')
plt.scatter(3/2, 3/2, color='red', label='Intersection (3/2, 3/2)')

plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of y = x and y = -x + 3')
plt.legend()
plt.grid(True)
plt.show()

The graph above shows the functions y = x and y = -x + 3. The red dot represents the intersection point at (3/2, 3/2).

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