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A periodic function is a function for which a specific horizontal shift, P, results in the original function: f ( x + P ) = f ( x ) for all values of x. When this occurs we call the smallest such horizontal shift with P > 0 the period of the function.
3.1.A Construct graphs of periodic relationships based on verbal representations. 3.2.B Describe key characteristics of a periodic function based on a verbal representation.
Definition. A function f is called periodic if its output values repeat at regular intervals. Graphically, this means that if the graph of f is shifted horizontally by p units, the new graph is identical to the original. Given a periodic function f: 1. The period is the horizontal distance that it takes for the graph to complete one full cycle.
Periodic phenomena are events that show repetitive pattern over time or space. Constructing graphs of periodic phenomena involves identifying the repeating pattern and period of the function. These can be derived from verbal representations or single cycles of the relationship.
For 1-3, identify the amplitude, period, phase shift and vertical shift of each function. 13 sin 4 x + E 1. f(x) = 25 — 10)) + 3 3. f (9) = 4— 9 sin 2 + — Amp: Period: Amp: 11 ... For 22-24, write the equation of the following sine curves. Use a positive leading coefficient a and the closest phase shift possible (left or right). For some ...
I. Determine the period, phase shift, and vertical shift, if any, of each function. 1. yx 4sec3( )S Vertical Stretch _____Period Vertical_____ Phase Shift _____ Shift _____ 2. yx 2csc2( )S Vertical Stretch _____Period Phase_____ Shift Vertical_____ Shift _____ 3. sec 4 yx §·S ¨¸ ©¹
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