Find Amplitude, Period, and Phase Shift y=-6tan(x)

Problem

y=−6*tan(x)

Solution

1. Identify the general form of the tangent function, which is y=A*tan(B*(x−C))+D

2. Determine the amplitude. For the tangent function y=A*tan(x) the amplitude is technically undefined because the function extends to infinity. However, the vertical stretch factor is |A|=|−6|=6

3. Calculate the period using the formula P=π/|B| In this equation, B=1

4. Solve for the period: P=π/1=π

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

Final Answer

Amplitude: None (Vertical Stretch: 6), Period: *π*, Phase Shift: 0

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