Which of the following is true for f(x) = -2sin(x) - 3?
The range of the function is the set of real numbers -2 is less than or equal to y and y is less than or equal to 2
The graph of the function is the graph of f(x) = -2sin(x) shifted 3 units up
The amplitude of the function is 2
The period of the function is 4pi

Solution:

Given function f(x) = -2sin(x) - 3

We know that the maximum value of sinx is 1 and the minimum value of sinx is -1.

So, the range will be as follows:

Minimum value: -2(-1) - 3 = 2 - 3 = -1

Maximum value: -2(1) - 3 = -2 - 3 = -5

So, the range is (-5, -1)

Now let us plot the graph by taking some sample values for x

This is the graph for f(x) = -2sin(x)

The graph of f(x) = -2sin(x) - 3 is as shown

Hence, we can say that the graph of f(x) = -2sin(x) is shifted 3 units up.

The remaining options are false.

Which of the following is true for f(x) = -2sin(x) - 3?

Summary:

The graph of f(x) = -2sin(x) is shifted 3 units up.