Find Amplitude, Period, and Phase Shift y=1+tan(1/2x)

Problem

y=1+tan(1/2*x)

Solution

1. Identify the standard form of the tangent function y=A*tan(B*(x−C))+D In this equation, A=1 B=1/2 C=0 and D=1

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|=1

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

P=π/(1/2)

P=2*π

4. Identify the phase shift C Since there is no horizontal shift inside the tangent argument, the phase shift is 0

Final Answer

Amplitude: None, Period: *2*π*, Phase Shift: *0

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