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=7xgiving any solution for x x\,x in terms of k k\,k and mmm.
