What are the important information needed to graph $y = 2 tan (3 π (x) + 4)$ $y=2 tan(3pi(x) +4)$ ?

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Answer 1 · 2018-07-11T01:30:42

As below.

Standard form of tangent function is $y = A tan (B x - C) + D$ $y = A tan (Bx - C) + D$

$Given : y = 2 tan (3 π ξ) + 4$ $"Given : " y = 2 tan (3 pi xi) + 4$

$A = 2, B = 3 π, C = 0, D = 4$ $A = 2, B = 3 pi, C = 0, D = 4$

$A m p l i t u d e = | A | = NONE for tangent function$ $Amplitude = |A| = "NONE for tangent function"$

$Period = \frac{π}{| B |} = \frac{π}{3 π} = \frac{1}{3}$ $"Period " = pi / |B| = pi/(3pi) = 1/3$

$Phase Shift = - \frac{C}{B} = \frac{0}{3 π} = 0, No Phase Shift$ $"Phase Shift " = -C / B = 0 / (3 pi) = 0, " No Phase Shift"$ #

$Vertical Shift = D = 4$ $"Vertical Shift " = D = 4$

graph{2 tan(3 pi x) + 6 [-10, 10, -5, 5]}

What are the important information needed to graph y=2tan(3π(x)+4)y=2 tan(3pi(x) +4) ?