Question

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

Answer 1

Answer: C

Step-by-step explanation: I just did it!

Answer 2

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

`f(x)=AsinB(x+C)+D`, where,

• A is the amplitude. Also, if A is negative, curve reflects about x axis
• B is the compression/stretching factor. It changes the period when it is a value other than 1.
• C is the phase shift. It translates curve left or right. Negative value shifts right and positive value shifts left.
• D is the vertical shift. It translates curve up or down. Negative value shifts down and positive value shifts up.

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
`f(x)=-2sin(x)` 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
`2\pi`, NOT
`4\pi`. So this is not correct.

ANSWER: C is true