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IB Maths: Functions and Graphs – Practice Paper 3 (10 Questions)
IB Maths: Functions and Graphs – Practice Paper 3 (10 Questions)
Paper 3 concentrates on transformations and inverses: vertical shifts, reflections, vertical stretches, the order of composites, and the domains of inverse quadratic and root functions.
Quick answer Ten items, about twenty-five minutes. Items 01 to 04 cover substitution, domain and range and basic transformations; items 05 to 07 cover composite order, a cube-root inverse and a vertical stretch; items 08 and 09 are a completed square and a root inverse; item 10 redoes inverse notation.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | 25 minutes |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: IB Maths: Functions and Graphs – Tutor Lesson Plan |
| Level | IB SL |
02 Questions (10 items)
- FoundationGiven f(x) = x squared minus three x, find f(4).
- FoundationState the domain and range of g(x) = 1 over x.
- FoundationThe graph of y = f(x) moves up by two units. What is the new equation?
- FoundationHow is the graph of y = -f(x) related to y = f(x)?
- Intermediatef(x) = 2x + 1 and g(x) = x – 3. Find f of g of x and its value at 4.
- Intermediatef(x) = x cubed. Find the inverse and the inverse at 27.
- IntermediateHow does the graph of y = 2f(x) differ from y = f(x)?
- ChallengeFor y = x squared minus four x plus seven, give the minimum and the range.
- Challengey = the square root of x plus 3 for x at least minus three. Find the inverse and its domain.
- Error redoA student treats the inverse at 2 as one over f of 2. With f(x) = 4x + 2, what is the inverse at 2?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | f(4) = 4 | Sixteen minus twelve is four. |
| 2 | domain x not 0, range y not 0 | The denominator cannot be zero and the fraction never reaches zero, so both sides exclude it. |
| 3 | y = f(x) + 2 | A vertical shift is added to the whole value, while a change inside the bracket shifts sideways. |
| 4 | a reflection in the x axis | Every y changes sign, so the curve flips over the x axis. |
| 5 | f(g(x)) = 2x – 5, and at 4 it is 3 | Do g first, then f: two times x minus three plus one; at four the result is three. |
| 6 | inverse is the cube root, and at 27 it is 3 | Cubing and taking a cube root undo each other, since three cubed is twenty-seven. |
| 7 | a vertical stretch by a factor of two | Every y doubles, so the curve stretches vertically and its x-intercepts stay put. |
| 8 | minimum 3 at x = 2, range y at least 3 | Completing the square gives a square plus three, so the least value is three. |
| 9 | inverse is x squared minus 3, domain x at least 0 | Squaring both sides gives x equal to y squared minus three, and the old range x at least zero becomes the new domain. |
| 10 | the inverse at 2 is 0 | The inverse is a function, not a reciprocal: solving four x plus two equals two gives zero, while the reciprocal would be one tenth. |
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.
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.
