Two acoustic sensors measure the power levels P1 P_1\,P1 and P2 P_2\,P2 at a distance x x\,x from a reference point. Given that k k\,k is a positive constant,
on separate diagrams, sketch the graph with equation
(i) y=4k−2∣x∣y = 4k - 2|x|y=4k−2∣x∣
(ii) y=∣6x−k∣y = |6x - k|y=∣6x−k∣
Show on each sketch the coordinates, in terms of kkk, of each point where the graph meets or cuts the axes.
Hence find, in terms of kkk, the values of x x\,x for which the power levels are equal, such that
∣6x−k∣=4k−2∣x∣ |6x - k| = 4k - 2|x| ∣6x−k∣=4k−2∣x∣giving your answers in simplest form.
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.