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Math Help - Rational Function Graph

  1. #1
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    Rational Function Graph

    Hey Guyzzz,
    I need help with a rational function question, I am given a graph with the following things on it:

    1) Vertical Asymptote: x = 1
    2) Horizontal Asymptote: y = 1 (The graph doesn cross this asymptote on the +ve. x- and y- axis SIDE)
    3) Y-Intercept: -4
    4) X-INtercept: -2 and 2
    5) Point Discontinuity: x = -5 and x = 8

    The Question is `Determine a possible equation for this graph.`
    I have even also attached the Graph that will help you guyz.

    Please, try your best to help me in solving this problem.
    Thank you.
    Attached Thumbnails Attached Thumbnails Rational Function Graph-rational-function-graph.jpg  
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  2. #2
    MHF Contributor
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    Quote Originally Posted by MordernWar2 View Post
    Hey Guyzzz,
    I need help with a rational function question, I am given a graph with the following things on it:

    1) Vertical Asymptote: x = 1

    the factor (x-1) in the denominator

    2) Horizontal Asymptote: y = 1 (The graph doesn cross this asymptote on the +ve. x- and y- axis SIDE)

    degree of numerator = degree of denominator and the ratio of leading coefficients = 1

    3) Y-Intercept: -4

    f(0) = -4

    4) X-INtercept: -2 and 2

    (x+2)(x-2) factors in the numerator

    5) Point Discontinuity: x = -5 and x = 8

    factors (x+5)(x-8) in both the numerator and denominator

    The Question is `Determine a possible equation for this graph.`
    I have even also attached the Graph that will help you guyz.

    Please, try your best to help me in solving this problem.
    Thank you.

    put it all together
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  3. #3
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    Hey Skeeter

    Hey Skeeter, I have put all othe them together, and here have a look at it.

    (x+2)(x-2)(x+5)(x-8) / (x-1)(x+5)(x-8)

    (x^2 -4)(x^2 - 3x - 40) / (x-1)(x^2 - 3x - 40)

    (x^4 - 3x^3 - 40x^2 - 4x^2 +12x + 160) / (x^3 - 3x^2 - 40x - x^2 + 3x + 40)

    (x^4 - 3x^3 - 44x^2  +12x + 160) / (x^3 - 4x^2 - 37x  + 40)

    And this is a totally different graph; it has an Oblique (Diagonal Asymptote) because the degree of the numerator is greater than (by 1) the degree of the denominator.

    So can you please tell how i would do this question?
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  4. #4
    Member Abu-Khalil's Avatar
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    f(x)=\frac{(x+2)(x-2)(x+5)(x-8)}{(x-1)^2(x+5)(x-8)}

    You didn't match numerator and denominator degrees.
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  5. #5
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    Thank You Very Much!!

    Hey Guyzzz,
    Thank you very much for helping m out here.
    I really appreciate it!!...


    Special thanks to Skeeter, and Mr. Fantastic for helping with both of my threads.
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