In a fluid dynamics simulation, the pressure deviation PPP at distance ddd from a source is modeled by the function
P(d)=d(d−k)(d−16) P(d) = d(d - k)(d - 16) P(d)=d(d−k)(d−16)where kkk is a constant such that 0<k<160 < k < 160<k<16.
Sketch the graph of y=P(d)y = P(d)y=P(d) on axes, showing the coordinates of the points where the graph meets the ddd-axis.
A secondary model suggests the pressure behaves according to the transformation y=P(−4d)y = P(-4d)y=P(−4d). Sketch this transformed graph on separate axes, showing the coordinates of the points where the graph meets the ddd-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.