How do you graph $y = - 2 sec (\frac{π x}{4} - \frac{π}{2})$ $y=-2sec((pix)/4-pi/2)$ ?

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Answer 1 · 2018-06-18T01:43:46

As below.

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

$Given : y = - 2 sec ((\frac{π}{4}) x - (\frac{π}{2}))$ $"Given : " y = -2 sec((pi/4)x - (pi/2))$

$A = - 2, B = \frac{π}{4}, C = \frac{π}{2}, D = 0$ $A = -2, B = pi/4, C = pi/2, D = 0$

$Amplitude = | A | = | - 2 | = 2$ $"Amplitude " = |A| = |-2| = 2$

$Period = \frac{2 π}{| B |} = \frac{2 π}{\frac{π}{4}} = 8$ $"Period " = (2pi) / |B| = (2pi) / (pi/4) = 8$

$Phase Shift = - \frac{C}{B} = \frac{- \frac{π}{2}}{\frac{π}{4}} = 2$ $"Phase Shift " = -C / B = (-pi/2) / (pi/4) = 2$

$Vertical Shift = D = 0$ $"Vertical Shift " = D = 0$

graph{-2 sec((pi/4)x - (pi/2)) [-10, 10, -5, 5]}

How do you graph y=−2sec(πx4−π2)y=-2sec((pix)/4-pi/2)?