What Does It Mean to Graph a Function?
A graph of a function is a visual representation of the relationship between input values () and output values ( or ). Every point on the graph has coordinates , where is in the domain of the function.
In IB Mathematics AI SL, you need to be comfortable both sketching graphs by hand and using technology (your GDC) to produce accurate graphs. Understanding the difference between these two approaches is essential.
The set of all points in the coordinate plane such that , where belongs to the domain of .
The graph gives you immediate visual information about a function's behavior — where it increases or decreases, where it crosses the axes, its maximum and minimum values, and how it behaves for large or small values of .
Sketching vs. Drawing: Know the Difference
IB exam questions will specifically ask you to either sketch or draw a graph. These words have different meanings and different expectations.
| Sketch | Draw | |
|---|---|---|
| Precision | Freehand, approximate | Accurate, to scale |
| Tools needed | Pen/pencil only | Ruler, possibly GDC output |
| What's required | Key features shown correctly | Precise coordinates plotted |
| Marks awarded for | Correct shape + labelled key features | Accurate positioning of all points |
When sketching, you must show:
- Correct general shape of the curve
- - and -intercepts (labelled with coordinates)
- Turning points / vertices (labelled)
- Asymptotes (drawn as dashed lines and labelled)
- Behaviour as
A very common mistake is treating a "sketch" as an excuse to draw something vague with no labels. In IB marking, a sketch must show all key features with coordinates clearly marked to earn full marks.