Question

Choose the function whose graph is given by: y AAAAA +2 O y A. y = cos(1 x) O B. y = cos( 3 ) O C. y = cos(2x) O D. y = cos(4x)

Answer 1

y = cos(4x)

Step-by-step explanation:

Given a cosine function in the below form;

`y=a\cos (bx)`

where;

Amplitude = |a|

Period = 2pi / |b|

Looking at the given graph, we can see that the amplitude(a) = 1, and the period is pi/2.

Let's go ahead and determine b as seen below;

`\begin{gathered} \text{Period}=(2\pi)/(|b|) \\ (\pi)/(2)=(2\pi)/(|b|) \\ |b|=(2\pi*2)/(\pi) \\ |b|=4 \\ b=4 \end{gathered}`

Since a = 1 and b = 4, the function whose graph is given can be written as;

`y=\cos (4x)`