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    IB Math AAHL
    /
    Transformations & asymptotes
    /

    Video

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    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

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    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Transformations & asymptotes

    Video Reviews

    Watch comprehensive video reviews for Transformations & asymptotes, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    HL content

    The video will automatically pause when it reaches a problem.

    Rationals with oblique asymptotes

    AHL 2.13

    When a rational function is of the form

    f(x)=dx+eax2+bx+c​

    there is a vertical asymptote at

    x=−de​🚫


    By performing polynomial division, we can find the oblique asymptote of f(x), which has the equation

    y=da​x+c

    for some constant c determined during the polynomial division.


    Example

    Find the asymptotes of 3x−15x2−3x+2​.


    There is a vertical asymptote at x=31​. To find the oblique asymptote, we performing the polynomial division:

    −5x2−3x 35​x−94​​3x−1)−05x2−3x+02−5x2+35​x​+02−34​x+02+34​x−94​​0914​​


    So the oblique asymptote has equation y=35​x−94​.

    Powered by Desmos

    Rationals with oblique asymptotes

    AHL 2.13

    When a rational function is of the form

    f(x)=dx+eax2+bx+c​

    there is a vertical asymptote at

    x=−de​🚫


    By performing polynomial division, we can find the oblique asymptote of f(x), which has the equation

    y=da​x+c

    for some constant c determined during the polynomial division.


    Example

    Find the asymptotes of 3x−15x2−3x+2​.


    There is a vertical asymptote at x=31​. To find the oblique asymptote, we performing the polynomial division:

    −5x2−3x 35​x−94​​3x−1)−05x2−3x+02−5x2+35​x​+02−34​x+02+34​x−94​​0914​​


    So the oblique asymptote has equation y=35​x−94​.

    Powered by Desmos

    HL content