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

Problem

y=−tan(3*x)

Solution

1. Identify the standard form of the tangent function y=A*tan(B*(x−C))+D In this expression, A=−1 B=3 C=0 and D=0

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|=1

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

4. Find the phase shift using the formula C/B Since C=0 the phase shift is 0

Final Answer

Amplitude: None (Vertical Stretch: 1), Period: π/3*, Phase Shift: 0

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