Question

Помогите построить график функции:у=tg2xобъясните он растянится или что?

Answer 1

КРАСНЫЙ у=tg2x

ФИОЛЕТОВЫЙ у=tgx

ГРАФИК СУЖАЕТСЯ

Answer 2

Building a Graph for the Function y = tan(2x)

To help you understand how to build a graph for the function y = tan(2x), let's start by discussing the properties of the tangent function and how the coefficient 2 affects the graph.

Tangent Function: The tangent function, denoted as tan(x), is a periodic function with a period of π. It has vertical asymptotes at odd multiples of π/2 and crosses the x-axis at even multiples of π.

Effect of Coefficient 2 (y = tan(2x)): When the coefficient 2 is applied to the independent variable x inside the tangent function, it affects the period of the function. The general formula for the period of the tangent function is given by π/b, where b is the coefficient of x. In this case, with y = tan(2x), the period is π/2.

Graphical Representation:

The graph of y = tan(2x) will have the following characteristics: 1. Period: The period of the function will be π/2, which means the graph will complete one full cycle in the interval from 0 to π/2. 2. Vertical Asymptotes: The vertical asymptotes will occur at odd multiples of π/4, which are the points where the function is undefined. 3. X-Intercepts: The function will have x-intercepts at the points where tan(2x) = 0, which are even multiples of π/2.

Conclusion:

In summary, the graph of y = tan(2x) will be a periodic function with a period of π/2, vertical asymptotes at odd multiples of π/4, and x-intercepts at even multiples of π/2. The coefficient 2 causes the function to complete one full cycle in a shorter interval compared to the standard tangent function.

Now, armed with this understanding, you can proceed to plot the graph of y = tan(2x. If you have specific values of x for which you'd like to see the corresponding y-values, feel free to ask for further assistance!