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

Problem

y=2*tan(x)

Solution

1. Identify the standard form of the tangent function, which is y=a*tan(b*(x−h))+k

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|=2

3. Calculate the period using the formula P=π/|b| Since b=1 the period is π/1=π

4. Find the phase shift by identifying the horizontal displacement h Since there is no value subtracted from x inside the tangent function, the phase shift is 0

Final Answer

Amplitude: None (Vertical Stretch: 2), Period: *π*, Phase Shift: 0

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