Find Amplitude, Period, and Phase Shift y=-3sec(x)

Problem

y=−3*sec(x)

Solution

1. Identify the standard form of the secant function, which is y=a*sec(b*(x−c))+d

2. Determine the amplitude. For the secant function, there is no amplitude in the traditional sense because the function is not bounded. However, the vertical stretch factor is |a|=|−3|=3

3. Calculate the period using the formula P=(2*π)/|b| Since b=1 the period is (2*π)/1=2*π

4. Find the phase shift by identifying the value of c Since there is no horizontal shift inside the function, c=0

Final Answer

Amplitude: None (Vertical Stretch: 3), Period: *2*π*, Phase Shift: 0

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