Question

Choose the function whose graph is given by:

Answer 1

The period of the function
`y=\cos (kx)` is
`T=(2\pi )/(k)`. From the graph you can see that period of given function is
`4\pi` (you can see that at x=0, y=1 and next time y=1 when x=4π ).

Then

`4\pi =(2\pi)/(k) ,\\ 4\pi k=2\pi,\\ k=(2\pi )/(4\pi ) =(1)/(2)`.

For
`k=(1)/(2)` the function
`y=\cos (kx)` becomes
`y=\cos ((1)/(2) x)`.

Answer: correct choice is A.

Answer 2

using a graph tool

I proceed to graph each case

case a)

`y=cos ((1)/(2) x)`

see the attached figure N 1

case b)

`y=cos ((1)/(4) x)`

see the attached figure N 2

case c)

`y=cos (4x)`

see the attached figure N 3

case d)

`y=cos (2x)`

see the attached figure N 4

therefore

the answer is the option A

`y=cos ((1)/(2) x)`