A research plan for sketching a graph
Study a function by a plan: domain, parity, zeros, increasing and decreasing, extreme points, then mark the key points of the graph.
- أوكرانيا: الصف ١٠
- روسيا: الصف ١١
- ألمانيا: الصف ١١
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
This follows the Ukrainian Grade 10 course (algebra and calculus, section 3, item 25, Graph sketching). A function is studied by a plan: 1) domain; 2) parity; 3) zeros; 4) intervals of increase and decrease; 5) extreme points; 6) other features. The graph is built from these data.
Example from the textbook: f(x) = (٣٢)x٢ − (١٤)x٣. Domain: D(f) = ℝ. The function is neither even nor odd. Zeros: x٢(٣٢ − x٤) = ٠, so x = 0 and x = 6. Derivative: f′(x) = (٣x٤)(٤ − x); the sign of f′ changes from − to + at 0 and from + to − at 4. So xmin = ٠, xmax = ٤, and f(٤) = ٨, f(٠) = ٠.
An even function has a graph symmetric about the y-axis, an odd one about the origin, so it is enough to study the function for x ⩾ 0.