`f(x) = cos(2x), g(x) = -cos(2x)` Describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts.
The graph of g(x) is a reflection of the graph of f(x) over the horizontal axis. The period, and amplitude are the same. This can also be described as a phase shift of pi units in either direction.
Note that the period of f(x) and g(x) is pi as opposed to h(x)=cos(x) which has a period of 2pi.
The graph of f(x) in black and g(x) in red: