A surveyor models the profile of a heavy suspension cable using the function H(x)=4∣x−5∣+12H(x) = 4|x - 5| + 12H(x)=4∣x−5∣+12, where H H\,H is the vertical clearance in metres above a reference line and x x\,x is the horizontal distance in metres from a support pillar. The point V V\,V represents the lowest point of the cable profile.
State the coordinates of VVV.
Use algebra to determine the set of values of x x\,x for which
4∣x−5∣+12>6x 4|x - 5| + 12 > 6x 4∣x−5∣+12>6x(Solutions relying on calculator technology are not acceptable.)
The support pillar is moved and the cable tension is adjusted such that the profile is transformed to the graph with equation y=12H(x−2)\displaystyle y = \frac{1}{2}H(x - 2)y=21H(x−2). Find the new coordinates of VVV.
471 exam-style questions on Edexcel A Level Maths Functions and Graphs, 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. Each one has a worked solution and a mark scheme showing where the marks go.