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Math Help - polynomial graph

  1. #1
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    polynomial graph

    I have a question:

    are all polynomial function has y-intercept and x-intercept?
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  2. #2
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    No they don't.

    Here's one without an x-intercept.

    f(x) = -x^2-5
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  3. #3
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    Quote Originally Posted by pickslides View Post
    No they don't.

    Here's one without an x-intercept.

    f(x) = -x^2-5

    that function looks like a linear. how about degree higher than 3?

    how about the y-intercept?
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    Quote Originally Posted by Anemori View Post
    that function looks like a linear.
    It is not linear, it is quadratic. Are you aware of the differences?


    Quote Originally Posted by Anemori View Post

    how about the y-intercept?
    My function has a y-intercept, you can find it by making x=0




    Quote Originally Posted by Anemori View Post
    how about degree higher than 3?
    g(x) = -x^4-5

    has order > 3 and no x-intercpets
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  5. #5
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    Quote Originally Posted by pickslides View Post
    It is not linear, it is quadratic. Are you aware of the differences?

    My function has a y-intercept, you can find it by making x=0

    g(x) = -x^4-5

    has order > 3 and no x-intercpets

    so in any polynomials y-intercept is always exist and x-intercept is not.
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  6. #6
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    The y-intercept is where x= 0. Since evaluating a polynomial involves only multiplication and addition or subtraction, which are possible for any real number, the domain of a polynomial always includes all real numbers, including 0.

    The x-intercept is where y, the value of the polynomial, is 0. Any polynomial of odd degree crosses the x-axis and so has an x-intercept. Polynomials of even degree may or may not have an x-intercept.
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    Quote Originally Posted by HallsofIvy View Post
    The y-intercept is where x= 0. Since evaluating a polynomial involves only multiplication and addition or subtraction, which are possible for any real number, the domain of a polynomial always includes all real numbers, including 0.

    The x-intercept is where y, the value of the polynomial, is 0. Any polynomial of odd degree crosses the x-axis and so has an x-intercept. Polynomials of even degree may or may not have an x-intercept.

    Thanks for the explanation.
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  8. #8
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    Quote Originally Posted by HallsofIvy View Post
    The y-intercept is where x= 0. Since evaluating a polynomial involves only multiplication and addition or subtraction, which are possible for any real number, the domain of a polynomial always includes all real numbers, including 0.

    The x-intercept is where y, the value of the polynomial, is 0. Any polynomial of odd degree crosses the x-axis and so has an x-intercept. Polynomials of even degree may or may not have an x-intercept.

    Hello here is one Polynomial rational function problem that does not have y-intercept.

     g(x) = \frac {2x-1}{x^2}

    can you verify that please. thanks!
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  9. #9
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    Quote Originally Posted by Anemori View Post
    Hello here is one Polynomial rational function problem that does not have y-intercept.

     g(x) = \frac {2x-1}{x^2}

    can you verify that please. thanks!
    true, it has an asymptote at x=0
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  10. #10
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    Quote Originally Posted by Anemori View Post
    Hello here is one Polynomial rational function problem that does not have y-intercept.

     g(x) = \frac {2x-1}{x^2}

    can you verify that please. thanks!
    you're mixing functions.

    polynomial functions are not rational functions.

    polynomial functions have the form ...

    f(x) = ax^n + bx^{n-1} + cx^{n-2} + ... + dx + e<br />

    and are defined for all real x.
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