IB Maths AA SL · Unit 2: Functions
IB Maths AA SL Transformations of Graphs Questions
Exam-style IB Maths AA SL transformations of graphs questions with worked solutions. Start with the 3 fully worked examples below — each is solved step by step the way an IB examiner expects — then try the practice questions and check your working against the mark scheme.
- 25 questions
- Paper 1: 18
- Paper 2: 7
- 6 easy
- 10 medium
- 4 hard
- 3 very hard
- 2 starter
- 3 worked examples
Practise Transformations of Graphs questions →
AA SL formula booklet
What's examined in AA SL transformations of graphs
The question bank covers these transformations of graphs question types (number of questions in brackets):
- Describing Transformations (12)
- Transforming Points (7)
- Deriving Transformed Functions (6)
Transformations of Graphs worked examples
Worked example 1: Mapping coordinates · easy
The point $P(4, -2)$ lies on $y = f(x)$. Find the coordinates of the image of $P$ under $y = f(x - 2) + 3$.
1. Analyse inner term $f(x - 2)$: horizontal translation of $2$ units RIGHT.
2. Apply to $x$: $4 + 2 = 6$.
3. Analyse outer term $+3$: vertical translation of $3$ units UP.
4. Apply to $y$: $-2 + 3 = 1$. Image: $\mathbf{(6, 1)}$.
Examiner tip: Transformations inside $f(\ldots)$ affect $x$ counter-intuitively (opposite direction to the sign). Transformations outside affect $y$ normally.
Worked example 2: Algebraic composition of transformations · medium
Given $f(x) = 3x^2 - 2x$, find $g(x)$ obtained by translating $f$ by the vector $\binom{2}{0}$ then applying a vertical stretch of scale factor $4$.
1. Translation: replace $x$ with $(x - 2)$: $f_1(x) = 3(x-2)^2 - 2(x-2)$.
2. Expand: $3(x^2 - 4x + 4) - 2x + 4 = 3x^2 - 12x + 12 - 2x + 4 = 3x^2 - 14x + 16$.
3. Vertical stretch by $4$: multiply the whole function by $4$: $g(x) = 4(3x^2 - 14x + 16)$.
4. Distribute: $\mathbf{g(x) = 12x^2 - 56x + 64}$.
Examiner tip: Always place $(x-c)$ inside parentheses before expanding; forgetting these brackets is the most common cause of transformation-expansion errors.
Worked example 3: Describing complex sequences · hard
Describe a sequence of three transformations mapping $f(x) = \sqrt{x}$ onto $g(x) = 3\sqrt{-x - 2}$.
1. Factorise inside: $g(x) = 3\sqrt{-(x + 2)}$.
2. Identify $(x+2)$: horizontal translation $2$ units left.
3. Identify the negative on $x$: reflection in the $y$-axis.
4. Identify the outer $\times 3$: vertical stretch scale factor $3$.
Examiner tip: When horizontal reflections and translations combine, always factor the negative sign INSIDE (i.e. $f(-(x+c))$) to read the correct translation direction.
Try these IB Maths AA SL transformations of graphs questions
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
Question 1 · easy · 5 marks · Paper 2
Let \(f(x) = x^2 - 4\). The graph of \(g(x)\) is obtained by translating the graph of \(f(x)\) by the vector \(\begin{pmatrix} -2 \\ 3 \end{pmatrix}\).
Find an expression for \(g(x)\), fully expanded.
Use your graphic display calculator to sketch both \(f(x)\) and \(g(x)\) on the same axes.
Find the exact coordinates of the vertex of the graph of \(g(x)\).
Question 2 · medium · 3 · Paper 1
Let $f(x) = 3x^2 - 2x$.
- Find an expression for $f(x - 2)$, giving your answer in the form $ax^2 + bx + c$. [2]
- Describe the single transformation that maps the graph of $y = f(x)$ onto the graph of $y = f(x - 2)$. [1]
Question 3 · hard · 6 marks · Paper 2
Consider the cubic function \(f(x) = -x^3 + 2x^2 + 5\). Let \(g(x) = f(x-2)\).
Use your GDC to find the coordinates of the local maximum and local minimum points on the graph of \(f(x)\).
Hence, write down the coordinates of the local maximum and local minimum points on the graph of \(g(x)\).
Find the coordinates of the two points of intersection between the graphs of \(f(x)\) and \(g(x)\).
All 25 transformations of graphs questions with mark schemes →
FAQ
How many IB Maths AA SL transformations of graphs questions are there?
There are 25 exam-style transformations of graphs questions in the AA SL question bank (Paper 1: 18 · Paper 2: 7), graded 6 easy, 10 medium, 4 hard, 3 very hard, 2 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Is transformations of graphs on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 18 · Paper 2: 7. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.
Where can I get the mark schemes?
Open the AA SL Unit 2 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.
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