A specialized hydraulic piston's displacement DDD (in mm) relative to a benchmark is modeled by the equation:
D(t)=25∣5t+8∣−6,t∈R D(t) = \frac{2}{5}|5t + 8| - 6, \quad t \in \mathbb{R} D(t)=52∣5t+8∣−6,t∈Rwhere t t\,t is the time in seconds.
State the coordinates of the vertex, VVV, of the graph of y=D(t)y = D(t)y=D(t).
Using algebra, determine the set of values of t t\,t for which
D(t)>2−15t D(t) > 2 - \frac{1}{5}t D(t)>2−51tSketch the graph with equation y=∣D(t)∣y = |D(t)|y=∣D(t)∣, stating the coordinates of the local maximum point and each local minimum point.
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.