Use a graphic display calculator (GDC) to graph the function, select a suitable viewing window, and apply its zero, minimum, maximum, intersection, and table tools. Always record coordinates and verify that apparent features are genuine rather than consequences of the chosen window.
This is SL 2.4: Features of a graph, applicable to GDC-active Paper 1 and Paper 2 questions.
| Feature | GDC method | What to report |
|---|---|---|
| Maximum or minimum | Graph the function, then use the maximum or minimum command. Set left and right bounds around the turning point. | The point ((x,y)), unless only the value is requested. |
| -intercept | Use the zero or root command, or find the intersection with . Repeat for every visible crossing. | . |
| -intercept | Calculate , or find the intersection with the -axis. | . |
| Vertical asymptote | Look for a discontinuity where values increase or decrease without bound. Use a table on both sides of the suspected value. | An equation such as . |
| Horizontal asymptote | Examine the graph or table for very large positive and negative -values and identify the value approached by . | An equation such as . |
For example, graph
Technology gives -intercepts and , and the -intercept . It also indicates vertical asymptotes and , a horizontal asymptote , and a local maximum at .
A common misconception is that every peak shown on the screen is a maximum. A GDC only searches within the selected interval, so adjust the window and check the stated domain. Also distinguish a maximum point ((x,y)) from the maximum value .
In an IB response, write the feature using correct mathematical notation, give coordinates where required, and use exact values or three significant figures unless instructed otherwise. Do not submit calculator menu output as the final answer.