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

F (x) = 5cos (1/2x) - 2

g (x) = 5cos (x) - 2

The period for a cosine function is 2pi/k

In the equation the k is located before the variable.

In g (x) we have 5cos (1x) - 2

so the period is 2pi/1 or 2pi. This means the length of one full period of cosine will go from 0 to 2pi.

In f (x) we have 5 cos (1/2 x) - 2

so the period is 2pi / (1/2) which is the same as 2pi * 2 or 4pi.

This means the period for the function is 4pi and the length of one full period of the cosine graph will go from 0 to 4pi.

The length of f (x) will be longer than that of g (x).