IB Maths AA HL AA 2.3 Rational, exponential and logarithmic functions questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper
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Difficulty
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Question 1

Paper 1, no calculatorEasy6 marks

Consider the functions

f(x)=1x,x≠0,g(x)=2x+3x−1,x≠1.f(x)=\frac1x,\quad x\ne 0, \qquad g(x)=\frac{2x+3}{x-1},\quad x\ne 1.
(a)

Write down f−1(x)f^{-1}(x)

[1]
(b)

State the equations of the vertical and horizontal asymptotes of the graph of y=g(x)y=g(x)

[2]
(c)

Sketch the graph of y=g(x)y=g(x) showing both asymptotes and all intercepts with the coordinate axes.

[3]

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