Question 525619: graph y=-3sec(pi/2x)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! graph y=-3sec(pi/2x)
The formula which is used to graph the sec function: y=Asec(Bx-C), Amplitude=A, period=2π/B, Phase-shift=C/B.
For given sec function:
Amplitude=3
B=π/2
Period=2π/(π/2)=4 radians
1/4 Period=1
Phase-shift: none
Graphing:
When graphing It would be helpful to relate to the more familiar cos function since sec is its reciprocal.
On the x-axis make tick marks at 1, 2, 3 and 4 representing four 1/4 periods or one period.
For the cos function,cos(pi/2x), you have these coordinates: (0,1), (1,0), (2,-1), (3,0), and(4,1)
For the sec function,sec(pi/2x), coordinates: (0,1), (1,∞), (2,-1), (3,∞), and (4,1)
Finally for the sec function,-3sec(pi/2x), multiply the y-coordinate by -3:
(0,-3), (1,asymptote), (2,3), (3,asymptote), and (4,-3)
..
Pictorially, the sec curve sits atop (touches the max) and below (touches the min) the cos curve
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