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S4 Maths: Transformations of Graphs (Paper 1 (basics))
S4 Maths: Transformations of Graphs (Paper 1 (basics))
Paper 1 (basics): ten graph-transformation questions with answers and one-line notes.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S4 Maths: Transformations of Graphs |
| Level | S4 |
02 Questions (10 items)
- FoundationThe graph of y = f(x) is translated 3 units upwards. Write the new equation and the image of (2, 5).
- FoundationThe graph of y = f(x) is translated 4 units to the right. Write the new equation and the image of (2, 5).
- FoundationThe graph of y = f(x) is translated 2 units downwards. What is the new equation and the image of (1, 7)?
- IntermediateReflect the graph of y = f(x) in the x-axis. Write the new equation and the image of (3, 4).
- IntermediateReflect the graph of y = f(x) in the y-axis. Write the new equation and the image of (3, 4).
- IntermediateThe graph of y = f(x) is stretched vertically by a factor of 2. Write the new equation and the image of (2, 5).
- ChallengeThe vertex of y = x squared is (0, 0). Write the equation after shifting the graph up 3 units and give the new vertex.
- ChallengeGive the vertex of y = (x – 2) squared and state the transformation from y = x squared.
- ChallengeHow does the graph of y = minus x squared differ from y = x squared? Give its opening direction and vertex.
- Error redoA student claims that y = f(x) + 3 shifts the graph 3 units to the right. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | y = f(x) + 3; the point moves to (2, 8) | A shift upwards is added outside the function, so the equation is y = f(x) + 3 and the y coordinate of the point becomes 5 plus 3, which is 8. |
| 2 | y = f(x – 4); the point moves to (6, 5) | A shift of h units to the right replaces x by x minus h, so the equation is f(x – 4); the x coordinate goes from 2 to 6 and y stays the same. |
| 3 | y = f(x) – 2; the point moves to (1, 5) | A shift downwards subtracts 2 outside the function, so the y coordinate changes from 7 to 5 while x stays the same. |
| 4 | y = -f(x); the point moves to (3, -4) | Reflecting in the x-axis replaces y by minus y, which is the same as putting a minus sign outside the function, so (3, 4) becomes (3, -4). |
| 5 | y = f(-x); the point moves to (-3, 4) | Reflecting in the y-axis replaces x by minus x, which is a change inside the function, so only the x coordinate changes sign. |
| 6 | y = 2f(x); the point moves to (2, 10) | A vertical stretch multiplies outside the function, so the y value doubles from 5 to 10 and x is unchanged. |
| 7 | y = x squared + 3, vertex (0, 3) | The vertex moves with the whole graph, so its y coordinate rises by 3 and it becomes (0, 3). |
| 8 | Vertex (2, 0); the graph of y = x squared is shifted 2 units to the right | The minus 2 sits inside the function and means a shift of 2 units to the right, so the vertex moves from (0, 0) to (2, 0). |
| 9 | It opens downwards and the vertex is still (0, 0) | The minus sign outside changes the sign of every y value, reflecting the graph in the x-axis, so it opens downwards while the vertex stays put. |
| 10 | The direction and the place of the change are both wrong: adding outside the function shifts the graph 3 units up, while horizontal shifts must change the variable. | Adding 3 outside raises every y value by 3, which is a vertical move; a horizontal shift needs a change such as f(x – 3) inside the function. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
For any graph transformation, first ask whether the change sits outside the function or inside it. Changes outside (adding k, multiplying by a, adding a minus sign) move the graph up or down, stretch it vertically or reflect it in the x-axis. Changes inside the variable (x plus h, x multiplied by k) move or stretch the graph horizontally, and the direction is the opposite of what most students expect: f(x + 3) shifts the graph 3 units to the left, not to the right. To track a single point, put its x into the inside change, feed the result into the outside change, and work out the new coordinates step by step instead of guessing. For two-step transformations, do the inside first and the outside second, because a different order gives a different image. Finish by checking that the vertex moved and the opening direction flipped correctly, then substitute a convenient value such as x = 0 to confirm.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
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