Key Idea: A graph is a visual summary of a function's behaviour. Topic 2.3 covers reading and drawing graphs — finding where they cross axes, where they intersect each other, and using the GDC effectively to get this information quickly. The ability to set an appropriate viewing window and read off values accurately is central to almost every Paper 2 question.
✅ Key graph features
📊 GDC graphing workflow
Example: Find x-intercepts of f(x) = 2x² − 3x − 5: GDC finds roots at x = −1 and x = 2.5 (or solve: (2x−5)(x+1)=0) Find where f(x) = x² and g(x) = 2x + 3 intersect: Graph both. GDC intersect → x = −1 (y = 1) and x = 3 (y = 9).
When reading intercepts from a graph: always double-check by substituting back. A GDC that shows a root at x = 2.00 should be confirmed as exact (check f(2) = 0) or written as approximate. Do not confuse x-intercept (y = 0) with y-intercept (x = 0). Both are visible on the graph but come from different substitutions.
Paper 2 (GDC allowed): Always sketch the graph in your answer, even roughly. Mark the intercepts and intersections you found. This earns method marks and helps you avoid misreading the GDC output. Paper 1 (GDC allowed): You will be given the graph and asked to read off coordinates, or given the equation and asked to find intercepts algebraically.