Question

Функции заданы формулами у=2х+1; у=х+7;у=2х-3; 1)Выпишите те функции . графики которых параллельны графику функции у=2х-1.Постройте их график

Answer 1

Параллельны к графику функции y=2x+1 и y=2x-3

Answer 2

To determine which functions have graphs parallel to the graph of the function $y=2x-1$, we need to find functions with the same slope (coefficient of $x$). The general form of a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

For the function $y = 2x - 1$, the slope $m$ is $2$.

Now let's check the other given functions to find parallel ones:

1. $y = 2x + 1$ - The slope is $m = 2$, so this function has the same slope as $y = 2x - 1$. The graphs of these functions are parallel.

2. $y = x + 7$ - The slope is $m = 1$, which is not equal to the slope of $y = 2x - 1$. Therefore, the graph of this function is not parallel to $y = 2x - 1$.

3. $y = 2x - 3$ - The slope is $m = 2$, so this function has the same slope as $y = 2x - 1$. The graphs of these functions are parallel.

So, the functions $y = 2x + 1$ and $y = 2x - 3$ have graphs that are parallel to the graph of $y = 2x - 1$.

Now let's plot these three functions to visualize their graphs.

To plot the graphs, we'll use the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

For $y = 2x - 1$:

• Slope ($m$) is $2$.
• Y-intercept ($b$) is $-1$.

For $y = 2x + 1$:

• Slope ($m$) is $2$.
• Y-intercept ($b$) is $1$.

For $y = 2x - 3$:

• Slope ($m$) is $2$.
• Y-intercept ($b$) is $-3$.

Let's plot these functions on the same graph:

(Note: The graph will be an approximation, and I'll use a limited range for $x$.)

pythonCopy code
import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-5, 5, 100)
y1 = 2 * x - 1
y2 = 2 * x + 1
y3 = 2 * x - 3

plt.plot(x, y1, label='y=2x-1', color='blue')
plt.plot(x, y2, label='y=2x+1', color='green')
plt.plot(x, y3, label='y=2x-3', color='red')

plt.xlabel('x')
plt.ylabel('y')
plt.title('Graphs of Functions')
plt.legend()
plt.grid(True)
plt.axhline(0, color='black', lw=0.5)
plt.axvline(0, color='black', lw=0.5)
plt.show()

The blue line represents the graph of $y=2x-1$, the green line represents the graph of $y=2x+1$, and the red line represents the graph of $y=2x-3$. As you can see, the blue and red lines (corresponding to $y=2x-1$ and $y=2x-3$) are parallel to each other, whereas the green line (corresponding to $y=2x+1$) is not parallel to the other two.