Find Amplitude, Period, and Phase Shift f(t)=-7tan(4t)

Problem

ƒ(t)=−7*tan(4*t)

Solution

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

2. Determine the amplitude. For the tangent function ƒ(t)=a*tan(b*t) the amplitude is technically undefined because the function range is (−∞,∞) However, the vertical stretch factor is |a|=|−7|=7

3. Calculate the period using the formula P=π/|b| Here, b=4

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

5. Identify the phase shift h Since there is no horizontal shift inside the argument of the tangent function (4*t is not in the form 4(t - h)),t*h*e*p*h*a*s(e)*s(h)*i*ƒ*t*i*s()$.

Final Answer

Amplitude: None (Vertical Stretch: 7), Period: π/4*, Phase Shift: 0

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