The strength of a radio signal SSS, measured in microvolts, is modelled by the function S(t)=32∣2t−10∣+4,t⩾0S(t) = \frac{3}{2}|2t - 10| + 4, \quad t \geqslant 0S(t)=23∣2t−10∣+4,t⩾0 where t t\,t is the time in seconds after a broadcast begins. The minimum signal strength occurs at point VVV.
Determine the coordinates of VVV.
Solve the equation S(t)=t+7S(t) = t + 7S(t)=t+7.
An interference signal is modelled by the equation S(t)=mt+1S(t) = mt + 1S(t)=mt+1 where m m\,m is a constant. Given that the broadcast signal and the interference signal have equal strength at exactly two distinct times,
find the range of possible values for 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.