Question

Построить график функции y= -3cos2x

Answer 1

Косинусоида, растянутая в 3 раза от оси х, сжатая в 2 раза к оси у и симметричная относительно оси х.

Answer 2

Graph of the Function y = -3cos(2x)

To graph the function y = -3cos(2x), we can use the properties of the cosine function. The general form of the cosine function is y = A cos(Bx + C) + D, where A, B, C, and D are constants that affect the graph. In this case, the function is y = -3cos(2x), so A = -3, B = 2, C = 0, and D = 0.

The coefficient A = -3 indicates that the graph will be reflected over the x-axis and vertically stretched by a factor of 3. The coefficient B = 2 indicates that the period of the function will be affected. The period of the function y = cos(x) is normally 2π, but with the coefficient 2, the period becomes π.

Let's plot the graph of the function y = -3cos(2x) to visualize its behavior.

Graph of y = -3cos(2x)

The graph of the function y = -3cos(2x) is a cosine function that has been reflected over the x-axis and vertically stretched by a factor of 3. The period of the function is π, which means the graph completes one full cycle from 0 to 2π.

The graph will be provided here based on the given function.

The graph will show the characteristic shape of a cosine function, but with the reflected and stretched features described by the coefficients -3 and 2, respectively.

This graph will help visualize how the function y = -3cos(2x) behaves and its relationship to the standard cosine function.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.