Question 843981: What is the x and y intercepts, the continuity, the behavior, and the vertical asymptotes of the function y=3-4csc(x-Pi/4)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What is the x and y intercepts, the continuity, the behavior, and the vertical asymptotes of the function
y=3-4csc(x-Pi/4)
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x-intercepts:: ?
Solve 3-4csc(x-(pi/4)) = 0
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csc(x-(pi/4)) = 3/4
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No angle has a csc of 3/4
No x- intercept
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y-intercept:: ?
Solve: y = 3 - 4csc(-pi/4)
csc(-pi/4) = 3/4
Ans: No y-intercept
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Vertical asymptotes:
csc has VA's when sin is 0; i.e. angle = 0 or pi
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Solve: x-(pi/4) = 0 or x-(pi/4) = pi
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x = pi/4 or x = (5/4)pi
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Continuity:: ?
Ans: Continuity broken where the vertical asymptotes occur.
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Cheers,
Stan H.
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