Question

How do you find the amplitude, period, and shift for `f(x) = -4 cos(3x - π) + 1`?

Answer 1

`4,(2pi)/3,pi/3,1`

Explanation:

`"the standard form of the cosine is"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=acos(bx+c)+d)color(white)(2/2)|)))`

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

`"phase shift "=-c/b," vertical shift "=d`

`"here "a=-4,b=3,c=-pi" and "d=1`

`rArr"amplitude "=|-4|=4," period "=(2pi)/3`

`"phase shift "=-(-pi)/3=pi/3," vertical shift "=+1`