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A-level Maths - How would you start to draw this reciprocal graph...?? Watch

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    Ok, so I'm having a silly moment and am having trouble drawing this graph...

    y=\frac{2x+1}{x-2}

    I know that the bottom part of the fraction translates the graph to the right by 2 as it "tends to infinity" on the x-axis at x=2.
    And that the bottom part of the graph crosses the axis at (-\frac{1}{2},0) and (0,-\frac{1}{2}).

    But I don't know how to draw the rest of the graph properly.
    Where on the y-axis does the reciprocal graph "tend to infinity"?
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    (Original post by Philip-flop)
    Ok, so I'm having a silly moment and am having trouble drawing this graph...

    y=\frac{2x+1}{x-2}

    I know that the bottom part of the fraction translates the graph to the right by 2 as it "tends to infinity" on the x-axis at x=2.
    And that the bottom part of the graph crosses the axis at (-\frac{1}{2},0) and (0,-\frac{1}{2}).

    But I don't know how to draw the rest of the graph properly.
    Where on the y-axis does the reciprocal graph "tend to infinity"?
    Divide top by bottom to get it in the form y=2 + A/(x-2)
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    It may be easier to sketch if you write y as  2+\frac{5}{x-2} .
    From here it is easy to see that the curve is just 1/x with a few simple transformations applied.
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    (Original post by tiny hobbit)
    Divide top by bottom to get it in the form y=2 + A/(x-2)
    Can you explain the process of dividing the top by the bottom? I don't think I'm following

    I ended up with y=-2+\frac{1}{x-2}

    I think I did something wrong?
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    (Original post by Philip-flop)
    Can you explain the process of dividing the top by the bottom? I don't think I'm following

    I ended up with y=-2+\frac{1}{x-2}

    I think I did something wrong?

    Basic long division, you should be able to do since you did chapter 1!
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    \frac{2x+1}{x-2} = \frac{2(x-2)+5}{x-2} = 2+\frac{5}{x-2}
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    (Original post by Naruke)
    Basic long division, you should be able to do since you did chapter 1!
    Oh yeah! I didn't think about dividing in that way! Managed to work out the answer straight away with the long division method.

    (Original post by solC)
    \frac{2x+1}{x-2} = \frac{2(x-2)+5}{x-2} = 2+\frac{5}{x-2}
    Thank you
 
 
 
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