Question

How do you graph and list the amplitude, period, phase shift for `y=-3sin(2x)-3`?

Answer 1

Amplitude = 3; period = `pi`, phase shift = 0; vertical shift = `-3`.

Explanation:

In general symbols,

for the oscillation y = a sin (b x +c ) + d,

Amplitude = `|a|`

period = `2/bpi`

Phase shift = #-c/b

Vertical shift = d.

Here, for #y = -3 sin (2x) - 3,

Amplitude = 3; period = `pi`, phase shift = 0; vertical shift = `-3`.

For the graph, this graph is topsy turvy ( due to negative sign ) of the

graph for

`y = 3sin 2x -3`

The axis of the wave is `y = -3`..

One half wave is from (0, -3) to (pi/2, -3),.

with the bisector nadir at (pi/4, -6).

The next half, for one full wave, is from (pi/2, -3) to (pi, -3), with

zenith ( crest ) at (3/4pi, 0).

Now, you can make it for this Table: I lack facility for making it, for

you.

`(x, y): (0, -3) (pi/4, -6) (pi/2, -3) (3/4pi, 0) (pi, -3)`

Either side outside, it is lateral (horizontal ) successive movement

of this single wave, through the period `pi`. .