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.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.