Which of the following is true for f(x)= -2sin(x)-3?
a) 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
b) the graph of the function is the graph of f(x)= -2sin(x) shifted 3 units up
c) the amplitude of the function is 2
d) the period of the function is 4pi

Let's write the general form of the sine curve:

, where,

Let's check the 4 choices.

A.

Since this curve's A is -2, its amplitude is 2 and range is from -2 to 2. BUT since D value is -3, it shifts vertically 3 units down making the range from -1 to -5. Clearly choice A is not true.

B.

This graph is the graph of shifted 3 units DOWN since D is negative. This choice isn't true.

C.

Because of the - (minus) sign in front of the function, the function is reflected about x-axis, but amplitude doesn't change. Since A value is 2, amplitude is 2. This is true.

D.

Period depends on the B value. Here, B value is 1, so period is normal as the parent function of a sine curve, which is , NOT . So this is not correct.

ANSWER: C is true

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step-by-step explanation: