IB Maths AI SL · Unit 2: Functions
Exam-style IB Maths AI SL graphing linear, quadratic, exponential and logarithmic functions 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.
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Slope, intercept, and interpreting the gradient in context. SL AI dresses linear models as taxi fares, phone plans, and rental costs — always ask what the gradient MEANS in the real-world context. Linear functions and modelling overview →
The question bank covers these graphing linear, quadratic, exponential and logarithmic functions question types (number of questions in brackets):
Consider $y = 2x - 8$. Find the exact coordinates of the $x$- and $y$-intercepts.
1. Set $x = 0$: $y = 2(0) - 8 = -8$.
2. State $y$-intercept: $(0, -8)$.
3. Set $y = 0$: $0 = 2x - 8$.
4. Solve: $2x = 8 \implies x = 4$.
5. State $x$-intercept: $(4, 0)$. Intercepts: $\mathbf{(4,\ 0)\text{ and }(0,\ -8)}$.
The parabola has equation $y = -x^2 + 6x - 5$. Find the exact coordinates of its vertex and $y$-intercept.
1. Read off the $y$-intercept via $x = 0$: $y = -5$, giving $(0, -5)$.
2. Vertex $x$: $x = \frac{-b}{2a} = \frac{-6}{-2} = 3$.
3. Substitute: $y = -(3)^2 + 6(3) - 5$.
4. Evaluate: $y = -9 + 18 - 5 = 4$.
5. State: vertex $\mathbf{(3,\ 4)}$; $y$-intercept $\mathbf{(0,\ -5)}$.
For $f(x) = 2^x - 8$, find the equation of the horizontal asymptote and the exact coordinates of the $x$-intercept.
1. Analyse: as $x \to -\infty$, $2^x \to 0$.
2. Asymptote: $y = 0 - 8 = -8$.
3. Set $f(x) = 0$: $0 = 2^x - 8 \implies 2^x = 8$.
4. Rewrite $8 = 2^3$: $2^x = 2^3 \implies x = 3$.
5. State: $x$-intercept $\mathbf{(3,\ 0)}$; asymptote $\mathbf{y = -8}$.
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
Consider the linear function \(f(x) = -0.5x + 3\).
Find the coordinates of the axes intercepts.
Sketch the graph of \(f(x)\) on the grid provided below.
Consider the exponential function \(h(x) = e^x - 3\).
Write down the equation of the horizontal asymptote.
Sketch the graph of \(h(x)\) on the grid below, showing the asymptote and axes intercepts.
Consider the exponential function \(f(x) = e^x\). The graph of \(f(x)\) is drawn below.
On the same grid, sketch the line \(y = x\).
Sketch the inverse function, \(f^{-1}(x)\), on the same grid.
Write down the mathematical equation of the inverse function.
There are 24 exam-style graphing linear, quadratic, exponential and logarithmic functions questions in the AI SL question bank (Paper 1: 16 · Paper 2: 8), graded 4 easy, 7 medium, 7 hard, 6 very hard. Every question has a full IB-style mark scheme (M, A and R marks).
Both. In the bank, Paper 1: 16 · Paper 2: 8. Practise with your GDC — AI papers expect calculator methods throughout.
Open the AI 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.