A laser displacement sensor is calibrated to measure the surface profile of a machined groove. The vertical height y y\,y relative to a datum, at a horizontal distance x x\,x from the start of the sensor's path, is modelled using two related functions.
Given that k k\,k and m m\,m are positive constants with k>mk > mk>m,
Sketch, on separate diagrams, the graph with equation
(i) y=∣3x−k∣y = |3x - k|y=∣3x−k∣
(ii) y=∣3x−k∣−my = |3x - k| - my=∣3x−k∣−m
Show on each sketch
Solve the equation
∣3x−k∣−m=7x|3x - k| - m = 7x∣3x−k∣−m=7x
giving any solution for x x\,x in terms of k k\,k and mmm.
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.