Find Amplitude, Period, and Phase Shift f(x)=tan(2x+1)

Problem

ƒ(x)=tan(2*x+1)

Solution

1. Identify the standard 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)=tan(x) the graph extends from negative infinity to positive infinity, so the amplitude is undefined.

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

4. Substitute the value b=2 into the period formula.

P=π/2

5. Calculate the phase shift using the formula Phase Shift=c/b

6. Identify the values from the expression 2*x+1 which can be written as 2*x−(−1) where b=2 and c=−1

Phase Shift=(−1)/2

Final Answer

Amplitude: None, Period: π/2*, Phase Shift: −1/2

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