You create a function sketch by plotting every given key feature, using the information to determine the graph’s shape, and then joining the features with an appropriate smooth curve. A sketch need not be exactly to scale, but it must show and label all mathematically relevant information.
A Reliable Sketching Method
For IB Mathematics: Analysis and Approaches, SL 2.3: Graphing, follow these steps:
- Draw and label the coordinate axes.
- Mark any stated intercepts, endpoints, stationary points or other coordinates.
- Draw and label any vertical, horizontal or oblique asymptotes.
- Use information about increasing, decreasing, symmetry or end behaviour to determine the curve’s shape.
- Join the features smoothly, without crossing an asymptote or creating unsupported turning points.
| Given information | What it tells you |
|---|---|
| An -intercept at | |
| A -intercept at | |
| Maximum or minimum at ((p,q)) | A turning point at ((p,q)) |
| The graph lies above the -axis | |
| The graph lies below the -axis | |
| Vertical asymptote | The curve approaches but does not cross |
| as | Horizontal asymptote on the right |
For example, suppose a parabola has roots and , vertex , and opens upwards. Plot , , and , then draw a smooth U-shaped curve symmetric about .
A common misconception is that a sketch can be vague because it is not precisely to scale. This is incorrect: unlike the command term draw, exact scaling is not required, but all stated features and the correct overall shape are required.
Exam Technique
This applies to AA SL and HL on Papers 1 and 2. Label intercepts, asymptotes and turning points clearly; an examiner should not have to infer which features you intended to show.