Question

How do you determine the amplitude, period, and shifts to graph `y=-sinx+2`?

Answer 1

`1,2pi,"vertical shift of"+2`

Explanation:

The standard form of the `color(blue)"sine wave function"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=asin(bx+c)+d)color(white)(a/a)|)))`

where amplitude = |a| , period`=(2pi)/b`

c is the horizontal shift and d , the vertical shift

here a = -1 , b = 1 , c = 0 and d = 2

hence amplitude = |-1| = 1 , period`=(2pi)/1=2pi`

there is no horizontal shift and vertical shift of `((0),(2))`