Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The general cosine function is given by

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

where $A=2$ is the amplitude,

$Period=\frac{2\pi}{B}$

$\Rightarrow 2\pi=\frac{2\pi}{B}$

$\Rightarrow B=1$,

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

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

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