A geophysicist is monitoring the normalized amplitude AAA of two different seismic waves over time ttt. Given that kkk is a positive constant,
on separate diagrams, sketch the graph with equation
(i) A=3k−2∣t∣A = 3k - 2|t|A=3k−2∣t∣
(ii) A=∣5t−k∣A = |5t - k|A=∣5t−k∣
Show on each sketch the coordinates, in terms of kkk, of each point where the graph meets or cuts the axes.
Hence determine, in terms of kkk, the values of ttt for which
∣5t−k∣=3k−2∣t∣|5t - k| = 3k - 2|t|∣5t−k∣=3k−2∣t∣
giving your answers in simplest form.
Practise Edexcel A Level Maths Functions and Graphs with exam-style questions for A Level Maths. 100 questions 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, matched to the Edexcel A Level Maths (9MA0) 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.