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  • Perplex
    IB Math AAHL
    /
    Transformations & asymptotes
    /

    Problem Bank

    [Maximum mark: 8]

    The function ​f​ is graphed over part of its domain on the coordinate axes below. The graph of ​y=f(x)​ has a horizontal asymptote at ​y=−1, two vertical asymptotes at ​x=1​ and ​x=−2, ​x​-intercepts at ​a​ and ​c​ where ​a<0<c, and a ​y​-intercept at ​b<0.


    1. Sketch the graph of ​y=∣f(∣x∣)∣​ on the axes above, indicating clearly any asymptotes or axes intercepts.

      [5]
    2. Find the possible values of ​k​ such that the equation ​[f(∣x∣)]2=k​ has exactly 2 solutions.

      [3]

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