What cosine function represents an amplitude of 2, a period of 2π, a horizontal shift of π, and a vertical shift of −1?

Question

asked Nov 25, 2017 148k views

1 Answer

Vibhav Singh Rohilla · Answer 1 · 2017-12-01T22:08:03+0000

Answer:

$f(x)=2\cos(x-\pi)-1$

Explanation:

The general cosine function is given by

$f(x)=A\cos(Bx-C)+D$

where
A=2 is the amplitude,

$Period=(2\pi)/(B)$

$\Rightarrow 2\pi=(2\pi)/(B)$

$\Rightarrow B=1$ ,

$c=\pi$ is the horizontal shift and
D=-1 is a downward vertical shift.

If we substitute all these values into the formula we obtain;

$f(x)=2\cos(x-\pi)-1$