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Thread: X & Y Intercepts

  1. #1
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    X & Y Intercepts

    Hey everyone, for this one I am suppose to find the x & y intercepts but what do I do if there is no Y intercept..

    $\displaystyle x^2y - xy +1 = x$
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  2. #2
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    $\displaystyle x^2y - xy +1 = x$

    $\displaystyle x^2y - xy = x-1$

    $\displaystyle y(x^2 - x) = x-1$

    $\displaystyle y = \frac{x-1}{(x^2 - x)}$

    $\displaystyle y = \frac{x-1}{x(x - 1)}$

    $\displaystyle y = \frac{1}{x}$

    what do you know about this function?
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  3. #3
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    Well this is just precalculus so would that mean that there is no Y intercept? I'm not sure because the problem states find the X & Y intercepts.
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  4. #4
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    You are correct $\displaystyle y = \frac{1}{x}$ has no X or Y intercepts

    You can see this by $\displaystyle x,y \neq 0$
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  5. #5
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    Quote Originally Posted by pickslides View Post
    $\displaystyle x^2y - xy +1 = x$

    $\displaystyle x^2y - xy = x-1$

    $\displaystyle y(x^2 - x) = x-1$

    $\displaystyle y = \frac{x-1}{(x^2 - x)}$

    $\displaystyle y = \frac{x-1}{x(x - 1)}$

    $\displaystyle y = \frac{1}{x}$ Mr F adds: $\displaystyle {\color{red}x \neq 1}$. The graph of this hyperbola has a hole at (1, 1).

    what do you know about this function?
    ..
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