Question

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

Answer 1

The graph of `f(x)` will have a period of `(2pi)/(1/2) = 4pi` will the graph of `g(x)` will have a period of `2pi`. This means that it will take `4pi` units for a crest or a trough to repeat itself in `f(x)` and only `2pi` in `g(x)`.

So essentially, `f(x)` has been horizontally stretched by a factor of `2`.

Here are the two graphs:

f(x)

graph{3cos(1/2x) - 5 [-20, 20, -10, 10]}

g(x)

graph{3cosx - 5 [-20, 20, -10, 10]}

Hopefully this helps!