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

Problem

y=tan(π*x)

Solution

1. Identify the standard form of the tangent function, which is y=A*tan(B*(x−C))+D

2. Determine the amplitude. For the tangent function y=tan(x) the graph extends from −∞ to ∞ so the amplitude is undefined.

3. Calculate the period using the formula P=π/|B| In this equation, B=π

4. Substitute the value of B into the period formula: P=π/π=1

5. Identify the phase shift. Since there is no horizontal shift C inside the function argument, the phase shift is 0

Final Answer

Amplitude: None, Period: 1, Phase Shift: 0

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