Question

Match each graph with me correct cosine function based on its period

Answer 1

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
`(P)/(|b|)`.

As we have the function y = cosx having period
`2\pi`. The graph will be as in figure 1 below.

Since, the next function is
`y=\cos (x)/(2)`. Therefore, the period of this function will be
`(2\pi)/(1/2)` i.e.
`4\pi`. So, the graph is given in figure 2 below.

Finally, the last function is
`y=\cos (x)/(4)`. Therefore, the period of this function will be
`(2\pi)/(1/4)` i.e.
`8\pi`. So, the graph is given in figure below.