Question

Постройте график функции y=arcsin 2x

Answer 1

График функции.................

Answer 2

Graph of y = arcsin(2x)

To graph the function y = arcsin(2x), we can start by understanding the parent function y = arcsin(x) and then apply the necessary transformations to graph y = arcsin(2x).

The parent function y = arcsin(x) represents the inverse of the sine function restricted to the domain [-1, 1] and the range [-π/2, π/2]. The function y = arcsin(x) is only defined for x in the closed interval [-1, 1].

Transformations

1. Horizontal Compression: The coefficient 2 in front of x in y = arcsin(2x) indicates a horizontal compression by a factor of 1/2.

Graphing Process

1. Start with the parent function y = arcsin(x). 2. Apply the horizontal compression by a factor of 1/2 to the parent function.

Let's plot the graph of y = arcsin(2x) based on the described transformations.

Graph:
- The graph of y = arcsin(2x) will be a horizontally compressed version of the graph of y = arcsin(x).
- The key points to consider are the points where the function is defined, which are within the interval [-1, 1].

Please note that the specific coordinates of the graph will depend on the scale chosen for the axes.

This graph will show the transformation of the parent function y = arcsin(x) to the function y = arcsin(2x) with the horizontal compression by a factor of 1/2.

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