Find Amplitude, Period, and Phase Shift f(x)=-4tan(2x)

Problem

ƒ(x)=−4*tan(2*x)

Solution

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

2. Determine the amplitude. For the tangent function ƒ(x)=a*tan(b*x) the amplitude is technically undefined because the function range is (−∞,∞) However, the vertical stretch factor is |a|=|−4|=4

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

4. Substitute the value of b into the period formula: P=π/2

5. Identify the phase shift h Since there is no horizontal shift inside the argument of the tangent function (it is simply 2*x, the phase shift is 0

Final Answer

Amplitude: None (Vertical Stretch: 4), Period: π/2*, Phase Shift: 0

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