IB Maths AA HL Topic 2: 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

Paper 1, no calculator Paper 2, calculator

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Question 1

Paper 1, no calculatorEasy6 marks

Consider the functions

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

(a)

Write down $f^{-1}(x)$

[1]

(b)

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

[2]

(c)

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

[3]

Question 2

Paper 2, calculatorEasy6 marks

For $x\in\mathbb{R}$ let $f(x)=x^2-2x$ and $g(x)=3$

(a)

Use a graphic display calculator to determine the $x$ -coordinates of the points of intersection of the graphs of $f$ and $g$ Hence solve $g(x)\geq f(x)$ giving your answer as an interval.

[3]

(b)

Solve $g(x)\geq f(x)$ algebraically.

[3]

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