The vertical displacement hhh (in decimetres) of an industrial piston at time ttt (where t∈Rt \in \mathbb{R}t∈R) is modelled by the cubic function:
h(t)=t(t−12)(t−k) h(t) = t(t - 12)(t - k) h(t)=t(t−12)(t−k)where kkk is a constant such that k>12k > 12k>12.
Sketch the graph of y=h(t)y = h(t)y=h(t) on a set of axes, labelling the coordinates of the points where the graph intersects the ttt-axis.
After a mechanical recalibration, the displacement is modelled by the transformed function g(t)=h(10−2t)g(t) = h(10 - 2t)g(t)=h(10−2t). Sketch the graph of y=g(t)y = g(t)y=g(t) on separate axes, labelling the coordinates of the points where the graph intersects the ttt-axis in terms of kkk.
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.