Answer:
It is required to match the functions given below with their graphs based on their periods.
We know that, 'period' of a function is the value where the graph repeats itself.
Also, if period of a function f(x) is P, then period of function f(bx) is [tex]\frac{P}{|b|}[/tex].
As we have the function y = cosx having period [tex]2\pi[/tex]. The graph will be as in figure 1 below.
Since, the next function is [tex]y=\cos \frac{x}{2}[/tex]. Therefore, the period of this function will be [tex]\frac{2\pi}{1/2}[/tex] i.e. [tex]4\pi[/tex]. So, the graph is given in figure 2 below.
Finally, the last function is [tex]y=\cos \frac{x}{4}[/tex]. Therefore, the period of this function will be [tex]\frac{2\pi}{1/4}[/tex] i.e. [tex]8\pi[/tex]. So, the graph is given in figure below.
