Free Rational functions questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Functions. Each question has the answer and the marking points an examiner would look for.
Generate a full Rational Functions worksheet →All Functions questionsThe graph of y = 1x is transformed to the graph of y = 1x + 3 + 2.
Describe the transformation.
State the domain and range of the new function.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | translation by −32 translation A1 by −32 A1 | 2 |
| (b) | x ≠ −3, y ≠ 2 domain x ≠ −3 A1 range y ≠ 2 A1 | 2 |
Consider f(x) = 3x + 2x − 2, x ≠ 2.
Write down the equations of the asymptotes of the graph of f.
Find the coordinates of the points where the graph crosses the axes.
Find f−1(x).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = 2, y = 3 x = 2 A1 y = 3 A1 | 2 |
| (b) | (−23, 0), (0, −1) x-intercept (−23, 0) A1 y-intercept (0, −1) A1 | 2 |
| (c) | 2x + 2x − 3 interchanging x and y M1 attempt to make y the subject M1 f−1(x) = 2x + 2x − 3 A1 | 3 |
The graph of y = 1x is transformed to the graph of y = 1x − 2 + 1.
Describe the transformation.
State the domain and range of the new function.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | translation by 21 translation A1 by 21 A1 | 2 |
| (b) | x ≠ 2, y ≠ 1 domain x ≠ 2 A1 range y ≠ 1 A1 | 2 |
Consider f(x) = −x + 5x − 1, x ≠ 1.
Write down the equations of the asymptotes of the graph of f.
Find the coordinates of the points where the graph crosses the axes.
Find f−1(x).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = 1, y = −1 x = 1 A1 y = −1 A1 | 2 |
| (b) | (5, 0), (0, −5) x-intercept (5, 0) A1 y-intercept (0, −5) A1 | 2 |
| (c) | x + 5x + 1 interchanging x and y M1 attempt to make y the subject M1 f−1(x) = x + 5x + 1 A1 | 3 |
The graph of y = 1x is transformed to the graph of y = 1x − 1 − 4.
Describe the transformation.
State the domain and range of the new function.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | translation by 1−4 translation A1 by 1−4 A1 | 2 |
| (b) | x ≠ 1, y ≠ −4 domain x ≠ 1 A1 range y ≠ −4 A1 | 2 |
Consider f(x) = x + 3x − 1, x ≠ 1.
Write down the equations of the asymptotes of the graph of f.
Find the coordinates of the points where the graph crosses the axes.
Find f−1(x).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = 1, y = 1 x = 1 A1 y = 1 A1 | 2 |
| (b) | (−3, 0), (0, −3) x-intercept (−3, 0) A1 y-intercept (0, −3) A1 | 2 |
| (c) | x + 3x − 1 interchanging x and y M1 attempt to make y the subject M1 f−1(x) = x + 3x − 1 A1 | 3 |
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Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in