Question

Построить график функции и исследовать его по графику : y=x^3-2 y=2x^2-6

Answer 1

Y=3x^3-2x^2+6x+3 
f(-x)=-f(x) функция нечетная 
график асимметричен относительно оси Оу 
точки пересечения с осями координат ???
y'=(3x^3-2x^2+6x+3)'=9x^2-4x+6; если у=0,то 9x^2-4^x+6=0; 
9x^2-4x+6=0; 
x(9x-4)=6; 
x=6; x=0,9 

Answer 2

Introduction

To plot and analyze the graph of the function y = x^3 - 2 and y = 2x^2 - 6, we will examine the characteristics of the functions and then plot them on a graph.

Analyzing the Functions

Let's analyze each function separately to understand their behavior.

For the function y = x^3 - 2: - The function is a cubic function. - The coefficient of x^3 is positive, indicating that the function has a positive leading coefficient. - The constant term is -2, indicating that the graph is shifted downward by 2 units. - The function is an odd function, meaning it is symmetric with respect to the origin. - The graph will pass through the point (0, -2) since the constant term is -2.

For the function y = 2x^2 - 6: - The function is a quadratic function. - The coefficient of x^2 is positive, indicating that the function has a positive leading coefficient. - The constant term is -6, indicating that the graph is shifted downward by 6 units. - The function is an even function, meaning it is symmetric with respect to the y-axis. - The graph will pass through the point (0, -6) since the constant term is -6.

Plotting the Graphs

Now, let's plot the graphs of the two functions on the same coordinate system:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-10, 10, 100)
y1 = x**3 - 2
y2 = 2*x**2 - 6

plt.plot(x, y1, label='y = x^3 - 2')
plt.plot(x, y2, label='y = 2x^2 - 6')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graphs of y = x^3 - 2 and y = 2x^2 - 6')
plt.legend()
plt.grid(True)
plt.show()

The graph will show the