A model for the elevation EEE (in decameters) of a section of a mountain range relative to a baseline is given by a polynomial function E=h(d)E = h(d)E=h(d), where ddd is the horizontal distance (in km) from a lookout point.
A sketch of the curve y=h(d)y = h(d)y=h(d) shows that it passes through the point (0,10)(0, 10)(0,10) on the yyy-axis and touches the xxx-axis at a minimum turning point (4,0)(4, 0)(4,0). There is a maximum turning point at (−4,16)(-4, 16)(−4,16). The function behaves like a positive cubic, falling as d→−∞d \rightarrow -\inftyd→−∞ and rising as d→∞d \rightarrow \inftyd→∞.
On separate diagrams, sketch the curve with the following equations:
y=2h(d−4)y = 2h(d - 4)y=2h(d−4)
y=h(2d)−10y = h(2d) - 10y=h(2d)−10
On each sketch, show clearly the coordinates of:
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.