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,

A is the amplitude. Also, if A is negative, curve reflects about x axisB 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 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

24 students walk to school

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute:

answer: the slope is equal -1.