Find Amplitude, Period, and Phase Shift y=sec(2x)

Problem

y=sec(2*x)

Solution

1. Identify the standard form of the function, which is y=a*sec(b*(x−h))+k For the given function y=sec(2*x) the parameters are a=1 b=2 h=0 and k=0

2. Determine the amplitude, which is technically undefined for the secant function because it does not have a maximum or minimum value. However, in the context of transformations, the vertical stretch factor is |a|=1

3. Calculate the period using the formula P=(2*π)/|b|

P=(2*π)/2

P=π

4. Find the phase shift by identifying the horizontal displacement h Since there is no value subtracted from or added to x inside the function, the phase shift is 0

Final Answer

Amplitude: None, Period: *π*, Phase Shift: *0

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