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  • Perplex
    IB Math AAHL
    /
    Function Theory
    /

    Problems

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    Problem Bank - Function Theory

    Access custom-built, exam-style problems for function theory. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 4
    1

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    0 / 6

    The graph of y=g(x) is shown in the following for −3≤x≤5.

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    1. Write down the value of g(3)

      [1]
    2. Find the value of

      1. (g∘g)(5)

        [2]
      2. (g−1∘g−1)(1)

        [1]
    3. Sketch the graph of y=g(x+1)−1 on the axes above.

      [2]
    2

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    Consider the functions f(x)=x3−1 and g(x)=2−3x.

    1. Write down the value of g−1(−7).

      [1]

    Let h(x)=(g∘f)(x)

    1. Find an expression for h(x).

      [2]
    2. Find h−1(−19).

      [3]
    3

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    0 / 4

    Consider the rational function g(x)=x−cax+b​ where a,b,c∈Z and x=c. The graph of y=g(x) is shown in the diagram below.

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    1. Write down

      1. the value of a,

        [1]
      2. The value of c.

        [1]
    2. Find the value of b.

      [2]
    4

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    0 / 6

    Consider the rational function g(x)=3+2x7−4x​, for x=−23​.

    1. For the graph of y=g(x) find

      1. the coordinates of the axes intercepts,

        [2]
      2. the equations of the asymptotes.

        [2]
    2. Hence sketch the graph of y=g(x) on the axes below.

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      [2]
    5

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