Find Amplitude, Period, and Phase Shift y=11tan(4x-2)

Problem

y=11*tan(4*x−2)

Solution

1. Identify the general form of the tangent function y=A*tan(B*x−C)+D where A=11 B=4 and C=2

2. Determine the amplitude. For the tangent function, the amplitude is technically undefined because the function extends to infinity; however, the vertical stretch factor is |A|=11

3. Calculate the period using the formula P=π/|B|

Period=π/4

4. Calculate the phase shift using the formula C/B

Phase Shift=2/4

5. Simplify the phase shift fraction.

Phase Shift=1/2

Final Answer

Amplitude: None (Vertical Stretch: 11), Period: π/4*, Phase Shift: 1/2

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