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  • Perplex
    IB Math AAHL
    /
    Cartesian plane & lines
    /

    Problem Bank

    [Maximum mark: 13]

    Consider the rational function ​f(x)=x+33x−1​, for ​x=−3.

    1. For the graph of ​y=f(x), find

      1. the ​x​-intercept,

        [1]

        To earn a crown, get your answer ready before you reveal the options!

      2. the ​y​-intercept,

        [1]
      3. the equation of the vertical asymptote,

        [1]
      4. the equation of the horizontal asymptote

        [1]

    The graph of ​y=f(x)​ intersects the line ​y=3−x​ at ​P​ and ​Q, where the ​x​-coordinate of ​P​ is less than that of ​Q.

    1. Find the coordinates of ​P​ and ​Q.

      [5]

    The line ​L​ is perpendicular to ​P​ and ​Q, and intersects ​y=3−x​ at point ​X, the midpoint of ​P​ and ​Q.

    1. Given that ​[PX]=[QX], find the equation of ​L​ in the form ​y=mx+c.

      [4]

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