Messing with the graph of cos (x).

The black line is f(x) = cos (x).

The line(s) in green are functions where f(x) = n cos(x) where n is some integer.

The line(s) in magenta are functions where f(x) = cos (nx) and n is some integer.

In the first class of functions, changing n changes the altitude
of the graph.
In the second class of functions, changing n changes the frequency
of the graph.

In the first class of functions, the y-coordinate is multiplied by n. This is because in y = cos (x), the y-value would be the cos (x), and so n cos (x) mulitiplies y by what it would have been.

In the second class of functions, the x-coordinates are multiplied by n. In a cyclical function like f(x) = cos (x), this is going to affect how quickly the y values repeat because you are multiplying the x's before the function operation.

Darron Steele, Created with GeoGebra