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

Problem

ƒ(x)=tan(2*x)

Solution

1. Identify the general form of the tangent function, which is ƒ(x)=a*tan(b*(x−c))+d

2. Determine the amplitude. For the tangent function, the amplitude is technically undefined because the function extends to infinity; however, the vertical stretch factor |a| is 1

3. Calculate the period using the formula P=π/|b| Here, b=2

P=π/2

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

Final Answer

Amplitude: None (Stretch Factor: 1), Period: π/2*, Phase Shift: 0

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