Question 197622: Okay, here it is.
Sketch the graph of the rational function.
y=(x-2)/(x-3)
I don't remember seeing problems like this, but I'm thinking that if this follows suite with some of the other problems I've done in this review packet, the x-3 on the bottom means the graph is shifted right 3 spaces, making the vertical asymptote x=3. I think the x-2 on the top tells us how close the two segments of the graph are to 0,0 (relative to where the asymptotes have moved the graph, that is).
Am I on the right track? any explanation would be greatly appreciated.
Thanks
-Dudewhoneedshelp
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Sketch the graph of the rational function.
y=(x-2)/(x-3)
I don't remember seeing problems like this, but I'm thinking that if this follows suite with some of the other problems I've done in this review packet, the x-3 on the bottom means the graph is shifted right 3 spaces, making the vertical asymptote x=3. I think the x-2 on the top tells us how close the two segments of the graph are to 0,0 (relative to where the asymptotes have moved the graph, that is).
Am I on the right track? any explanation would be greatly appreciated.
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Yes, the function has a vertical asymptote at x=3 because when
x = 3 the denominator is zero so the function is undefined at x = 3.
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Let x = 0, then y = 2/3 is the y-intercept.
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Let y = 0, then x = 2 is the x-intercept.
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The horizontal asymptote is y = x/x = 1.
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Sketch all those factors and see if you can sketch the curve.
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Cheers,
Stan H.
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