Question

How does the graph of f(x)=3cos(1/2x)-5 differ from the graph of g(x)=3cos(x)-5?

Answer 1

The 2 graphs look the same, EXCEPT that the one with x coefficient (1/2) will be STRETCHED horizontally.

Answer 2

The period of f(x) is twice the period of g(x).

Explanation:

Refer the graphs shown below we have,

`3cos\left ( (1)/(2)x\right )-5\texttt{ in red colour}\\\\3cosx-5\texttt{ in blue colour}`

We can see from graph that the period of f(x)=3cos(x/2)-5 is two times of g(x)=3cos(x)-5.

The period of f(x) is twice the period of g(x).