Key Idea: Graphing means sketching a function with its key features labelled — not plotting every point. Sketch questions appear on both papers; on Paper 2 you graph it on the GDC first, then transfer the labelled features to paper.
📋 The sketch checklist
Intercepts — where it crosses each axis (label the coordinates). Turning points — any maximum or minimum (label the coordinates). Asymptotes — dashed guide lines the curve approaches (label their equations). Shape / end-behaviour — the right direction, set by the leading term. Marks come from the labelled features — a correctly-shaped curve with no values earns almost nothing.
| Feature | How to find it |
|---|---|
| y-intercept | Set x = 0 and read off y. |
| x-intercepts (zeros/roots) | Set y = 0 and solve. Factored form (x − a)(x − b) gives roots x = a, x = b for free. |
| Vertex (quadratic) | Axis of symmetry x = −b/(2a); substitute back for y. |
| Vertical asymptote | Where a denominator = 0 — dashed vertical line. |
| Horizontal asymptote | The value the curve levels off to (e.g. y = aˣ approaches y = 0). |
Tip: The highest-power term sets the shape: a quadratic with a > 0 opens up (minimum), a < 0 opens down (maximum); a positive x³ falls on the left and rises on the right.
✏️ IB-style worked examples
IB-style question — find the intercepts and vertex for a sketch
Find the intercepts and vertex of y = (x − 2)(x + 4) so it can be sketched.
Step by step:
x-intercepts: set y = 0 — each bracket gives a root.
y-intercept: set x = 0.
Vertex on the axis of symmetry, midway between the roots.
Through (2, 0), (−4, 0) and (0, −8); minimum vertex (−1, −9).
IB-style question — state the asymptotes for a sketch
State the asymptotes for a sketch of y = 1/(x + 3) − 2.
Step by step:
Vertical asymptote: denominator zero.
Horizontal asymptote: the −2 is the level the curve approaches.
Dashed lines x = −3 and y = −2; two branches approach them.
IB-style question — graph on the GDC, then transfer (Paper 2)
On Paper 2, sketch f(x) = x² − 6x + 5 for −1 ≤ x ≤ 7, labelling the intercepts and the minimum.
Step by step:
Graph it on the GDC and set a window that shows every feature.
Use 2:zero for the x-intercepts and 3:minimum for the turning point.
y-intercept from x = 0.
Upward parabola through (1, 0), (5, 0), (0, 5); minimum (3, −4).
🔒 GDC walkthrough
Step through the exact calculator keystrokes, screen by screen, in study mode.
Important: Copying the right curve shape isn't enough. A sketch earns its marks from the labelled features — write the coordinates of every intercept and turning point, and the equations of the asymptotes (e.g. x = −3, y = −2). On Paper 2, transfer the numbers off the GDC, not just the picture.
Tap each card to reveal the answer.
How do you find the y-intercept? Set x = 0 and read off the y-value.
x-intercepts of y = (x − 5)(x + 1) x = 5 and x = −1 — each bracket is zero, no solving needed.
Does y = −2x² + 3 open up or down? Down (a maximum) — the leading coefficient −2 is negative.
Vertical asymptote of y = 1/(x − 4) x = 4 — where the denominator equals 0.
Horizontal asymptote of y = 3ˣ y = 0 — the curve approaches the x-axis but never touches it.
Which GDC tool reads a turning point? 2nd → TRACE → 3:minimum (or 4:maximum) — then bound it with ENTER.
Exam tips
- Run the checklist every time: intercepts, turning points, asymptotes, shape.
- y-intercept ← set x = 0; x-intercepts ← set y = 0 (factored form gives roots free).
- Leading term sets the direction: a > 0 opens up, a < 0 opens down.
- Draw asymptotes as dashed lines and label their equations.
- Paper 2: graph on the GDC, window it, then transfer the labelled numbers — not just the shape.