Free Transformations of graphs 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 Transformations of Graphs worksheet →All Functions questionsThe graph of y = x2 is stretched vertically by scale factor 3 and then translated by 31. Write the equation of the new graph in the form y = ax2 + bx + c.
| Part | Answer and marking points | Marks |
|---|---|---|
| y = 3x2 − 18x + 28 stretch: y = 3x2 A1 translation: y = 3(x − 3)2 + 1 M1A1 expanded correctly A1 | 4 |
The point P(4, 4) lies on the graph of y = f(x). The graph of y = f(x) is transformed to the graph of y = 2f(3x + 9) + 5.
Find the coordinates of the image of P.
Describe fully a sequence of transformations that maps the graph of y = f(x) onto this graph.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (−53, 13) 3x + 9 = 4 (M1) x = −53 A1 y = 13 A1 | 3 |
| (b) | horizontal stretch, scale factor 13, then horizontal translation of −3; vertical stretch, scale factor 2; vertical translation of 5 horizontal stretch, scale factor 13 A1 followed by a horizontal translation of −3 (or: translation of −9 first, then the stretch) A1 vertical stretch, scale factor 2 A1 vertical translation of 5 (after the vertical stretch) A1 | 4 |
The graph of y = f(x) passes through the point P(4, 2).
The graph of y = f(x) is translated by −2−1. Find the image of P.
The graph of y = f(x) is transformed to y = 3f(x − 1). Find the image of P.
Describe fully a transformation that maps y = f(x) onto y = f(−x).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (2, 1) x-coordinate 2 A1 y-coordinate 1 A1 | 2 |
| (b) | (5, 6) x: 5 A1 y: 6 A1 | 2 |
| (c) | reflection in the y-axis reflection in the y-axis A1 | 1 |
The graph of y = x2 is stretched vertically by scale factor 2 and then translated by 1−3. Write the equation of the new graph in the form y = ax2 + bx + c.
| Part | Answer and marking points | Marks |
|---|---|---|
| y = 2x2 − 4x − 1 stretch: y = 2x2 A1 translation: y = 2(x − 1)2 − 3 M1A1 expanded correctly A1 | 4 |
The point P(−1, 4) lies on the graph of y = f(x). The graph of y = f(x) is transformed to the graph of y = −f(3x + 3) − 2.
Find the coordinates of the image of P.
Describe fully a sequence of transformations that maps the graph of y = f(x) onto this graph.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (−43, −6) 3x + 3 = −1 (M1) x = −43 A1 y = −6 A1 | 3 |
| (b) | horizontal stretch, scale factor 13, then horizontal translation of −1; reflection in the x-axis and no vertical stretch; vertical translation of −2 horizontal stretch, scale factor 13 A1 followed by a horizontal translation of −1 (or: translation of −3 first, then the stretch) A1 reflection in the x-axis and no vertical stretch A1 vertical translation of −2 (after the vertical stretch) A1 | 4 |
The graph of y = f(x) passes through the point P(1, 3).
The graph of y = f(x) is translated by 1−2. Find the image of P.
The graph of y = f(x) is transformed to y = 2f(x − 1). Find the image of P.
Describe fully a transformation that maps y = f(x) onto y = f(−x).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (2, 1) x-coordinate 2 A1 y-coordinate 1 A1 | 2 |
| (b) | (2, 6) x: 2 A1 y: 6 A1 | 2 |
| (c) | reflection in the y-axis reflection in the y-axis A1 | 1 |
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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