Find Amplitude, Period, and Phase Shift y=3tan(2x-pi)+1

Problem

y=3*tan(2*x−π)+1

Solution

1. Identify the standard form of the tangent function y=A*tan(B*(x−C))+D where A relates to the vertical stretch, B determines the period, C is the phase shift, and D is the vertical shift.

2. Determine the amplitude. For the tangent function y=tan(x) the graph extends from −∞ to ∞ vertically, so the concept of amplitude (half the distance between maximum and minimum values) does not apply.

3. Factor the expression inside the tangent function to find the horizontal components.

y=3*tan(2*(x−π/2))+1

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

P=π/2

5. Identify the phase shift from the factored form x−C

C=π/2

Final Answer

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

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