Question

Постройте в одной системе координат графики функций и сделайте вывод о взаимном расположении построенных графиков y=3/x и y= -3/x

Answer 1

Красный y=2/x, синий y=-2/x
Оба графика симметричны относительно начала координат

Answer 2

Plotting the Functions y=3/x and y=-3/x in the Same Coordinate System

To plot the functions \(y=\frac{3}{x}\) and \(y=-\frac{3}{x}\) in the same coordinate system, we can analyze their behavior and then graph them accordingly.

Behavior of the Functions: - The function \(y=\frac{3}{x}\) will have a positive value for \(y\) when \(x\) is positive, and a negative value for \(y\) when \(x\) is negative. - The function \(y=-\frac{3}{x}\) will have a negative value for \(y\) when \(x\) is positive, and a positive value for \(y\) when \(x\) is negative.

Plotting the Functions: - As both functions have a vertical asymptote at \(x=0\), we will consider the behavior of the functions for positive and negative values of \(x\). - For positive values of \(x\), the function \(y=\frac{3}{x}\) will be positive, and the function \(y=-\frac{3}{x}\) will be negative. - For negative values of \(x\), the function \(y=\frac{3}{x}\) will be negative, and the function \(y=-\frac{3}{x}\) will be positive.

Conclusion: - The graphs of the functions \(y=\frac{3}{x}\) and \(y=-\frac{3}{x}\) will be symmetric about the origin, with one function in the first and third quadrants, and the other in the second and fourth quadrants.

Let's plot the functions in the same coordinate system to visualize their behavior.