A signal processor measures the deviation of a frequency signal t t\,t from a set point. The response function R(t)R(t)R(t) is modelled by R(t)=∣3t−a∣−bR(t) = |3t - a| - bR(t)=∣3t−a∣−b, where a a\,a and b b\,b are positive constants with a>ba > ba>b.
Sketch, on separate diagrams, the graphs of the functions defined by:
(i) y=∣3t−a∣y = |3t - a|y=∣3t−a∣
(ii) y=∣3t−a∣−by = |3t - a| - by=∣3t−a∣−b
On each sketch, clearly label the coordinates of the minimum point and the point at which the graph intersects the yyy-axis.
Solve the equation
∣3t−a∣−b=5t |3t - a| - b = 5t ∣3t−a∣−b=5tgiving your answer for t t\,t in terms of a a\,a and bbb.
