`f(x) = cos(4x), g(x) = -2 + cos(4x)` Describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts.

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caledon eNotes educator| Certified Educator

Amplitude for both graphs: 1

Period for both graphs: pi/2

The graphs are identical, except that the graph of -2 + cos (4x) is shifted 2 units on the negative Y axis due to the inclusion of the -2 + value. 

cos4x in red, -2 + cos4x in yellow