The variables y y\,y and x x\,x are such that y y\,y is inversely proportional to x2x^2x2.
When x=3x = 3x=3, y=2y = 2y=2.
Find an equation for y y\,y in terms of xxx.
Sketch the graph of y y\,y against x x\,x for x>0x > 0x>0, stating the equations of the asymptotes.
33 exam-style questions on OCR (MEI) A Level Maths 1.4 Graphs, covering 1.4.1 Graphs of functions, 1.4.2 Intersection points with axes, 1.4.3 Completing the square for a quadratic curve, 1.4.4 Sketch graphs of simple functions, 1.4.5 Stationary points when curve sketching, 1.4.6 Graphs of reciprocal-type functions, 1.4.7 Single transformations of graphs, 1.4.8 Combined transformations of graphs (A-level only), and 1.4.9 Stationary points of inflection (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.