Question

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

Answer 1

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 $\frac{P}{|b|}$.

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 $y=\cos \frac{x}{2}$. Therefore, the period of this function will be $\frac{2\pi}{1/2}$ i.e. $4\pi$. So, the graph is given in figure 2 below.

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