Question

Спасайте! Построить график функции у=3соs2x.

Answer 1

Y=3cos2x
D(y)∈R
E(y)=3*[-1;1]=[-3;3]
T=2π/k=2π/2=π
Строим y=cosx
Сжимаем по оси ох в 2 раза
Растягиваем по оси оу в 3 раза
Чертеж во вложении

Answer 2

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

To graph the function y = 3cos(2x), we can start by understanding the properties of the cosine function and how it affects the graph when multiplied by a constant.

Properties of the Cosine Function: The cosine function, cos(x), is a periodic function with a period of 2π. It oscillates between -1 and 1 as x varies.

Effect of the Constant Multiplier: When a constant is multiplied to the cosine function, it affects the amplitude of the graph. In this case, the constant 3 will affect the amplitude of the cosine function.

Graphing Process

1. Amplitude: The amplitude of the function y = 3cos(2x) is 3. This means the graph will oscillate between -3 and 3.

2. Period: The period of the function y = 3cos(2x) is affected by the coefficient of x inside the cosine function. The period is calculated using the formula 2π/b, where b is the coefficient of x. In this case, the period is 2π/2 = π.

3. Phase Shift: There is no phase shift in the function y = 3cos(2x) because there is no additional constant added or subtracted inside the cosine function.

4. Vertical Shift: The function y = 3cos(2x) does not have a vertical shift because there is no constant added or subtracted outside the cosine function.

Graph of y = 3cos(2x)

Now, let's plot the graph of the function y = 3cos(2x) based on the properties we've discussed.

The graph will be a cosine function with an amplitude of 3, a period of π, no phase shift, and no vertical shift.

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