Question 771312: Please state the period and 2 consecutive asymptotes of the two graphs.
1. y= -3tan(pi*x)
2. y= 2sec(4x)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Please state the period and 2 consecutive asymptotes of the two graphs.
1. y= -3tan(pi*x)
equation of tan function: y=tan(Bx-C), period=pi/B, phase shift=C/B
For given function: y= -3tan(pi*x)
period=pi/B=pi/pi=1
..
asymptotes occur when the function is undefined
tan(pix)=sin(pix)/cos(pix)
tan(pix) becomes undefined when cos(pix)=0
..
cos(pi/2)=0
pix=pi/2
x=1/2
..
cos(3pi/2)=0
pix=3pi/2
x=3/2
2 consecutive asymptotes: x=1/2, x=3/2
...
2. y= 2sec(4x)
equation of sec function: y=sec(Bx-C), period=2pi/B, phase shift=C
For given function: y= 2sec(4x)
period=2pi/B=2pi/4=pi/2
sec=1/cos
asymptotes occur when cos(4x)=0
..
cos(pi/2)=0
4x=pi/2
x=pi/8
..
cos(3pi/2)=0
4x=3pi/2
x=3pi/8
2 consecutive asymptotes: x=pi/8, x=3pi/8
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