`f(x) = cos(2x), g(x) = -cos(2x)` Describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts.

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embizze eNotes educator| Certified Educator

f(x)=cos(2x); g(x)=-cos(2x)

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: