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

Mathematics

2 answers:

serious [3.7K]2 years ago

5 0

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.

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.

This graph is the graph of $f(x)=-2sin(x)$ shifted 3 units DOWN since D is negative. This choice isn't true.

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.

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.