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:
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.