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.
471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.