Find Amplitude, Period, and Phase Shift f(x)=5tan(2x)

Problem

ƒ(x)=5*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 ƒ(x)=a*tan(b*x−c)+d the amplitude is technically undefined because the function extends to infinity; however, the vertical stretch factor is |a|=|5|=5

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

4. Substitute the value b=2 into the period formula to get P=π/2

5. Calculate the phase shift using the formula c/b

6. Substitute the value c=0 and b=2 into the phase shift formula to get 0/2=0

Final Answer

Amplitude: None (Vertical Stretch: 5), Period: π/2*, Phase Shift: 0

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