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.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
