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Thread: algebraic fractions /functions question

  1. #1
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    algebraic fractions /functions question

    So it is clear to me that something like (x^2 - 5x+ 6)/ (x-3) simplifies to x-2

    But if i now think about the function f(x) = (x^2 - 5x+ 6)/(x-3) and explores the sketch on a graph plotter , it draws a straight line x-2,
    I know there is a problem at x=3 but are we saying the two things are equivalent or not?
    So what is the sketch of f(x) if it is not a line?
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  2. #2
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    Re: algebraic fractions /functions question

    The graph of y= \frac{x^2- 5x+ 6}{x- 3} is a "straight line with a hole in it".

    \frac{x^2- 5x+ 6}{x- 3}= x- 2 for all x except x= 3. There is no value at x= 3 because when x= 3, y= \frac{0}{0} which is "undefined".

    On a "graph plotter" you don't see the "hole" because it is a single point.
    Last edited by HallsofIvy; Nov 3rd 2017 at 04:20 AM.
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  3. #3
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    Re: algebraic fractions /functions question

    Thanks, i thought it must be something like this! A bit deep this stuff
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