Key Idea: Topic 2.4 is about describing the shape and behaviour of a graph: where it rises, where it falls, where it peaks or troughs, and how it behaves at its extremes. A local maximum is a peak โ the function is higher there than at nearby points. A local minimum is a trough. An asymptote is a line the graph approaches but never reaches.
โ Graph features and what they tell you
Example: Describe f(x) = xยณ โ 3x: GDC shows: local max at (โ1, 2), local min at (1, โ2). Increasing on: x < โ1 and x > 1. Decreasing on: โ1 < x < 1. Exponential: f(x) = 3โปหฃ + 1: As x โ โ, 3โปหฃ โ 0, so f(x) โ 1. Horizontal asymptote: y = 1 (the graph gets closer and closer but never reaches 1).
When describing increasing/decreasing intervals, use the x-values (not y-values) for the interval. A function can have more than one local maximum or minimum โ use the GDC to find all of them within the domain shown.
Paper 2 (GDC allowed): Use the GDC 'maximum' and 'minimum' functions to find turning point coordinates. Then state the intervals of increase/decrease around those points. Paper 1: You may be given a sketch and asked to describe features in words. Use precise vocabulary: 'local maximum at x = 2, f(2) = 5', not just 'it goes up then down'.