The altitude hhh of a surveying drone, measured in decameters relative to a reference level, is modeled by the function y=f(x)y = \mathrm{f}(x)y=f(x), where xxx represents the horizontal displacement from a base station. The graph of this function, curve CCC, is characterized by the following properties:
State the equation of the asymptote to the curve with equation y=f(−x)y = \mathrm{f}(-x)y=f(−x).
State the coordinates of the turning point on the curve with equation y=f(2.5x)y = \mathrm{f}(2.5x)y=f(2.5x).
Given that the line with equation y=ky = ky=k, where kkk is a constant, intersects CCC at exactly one point,
state the possible values for kkk.
The curve CCC is transformed to a new curve that passes through the origin.
(i) Given that the new curve has equation y=f(x)−ay = \mathrm{f}(x) - ay=f(x)−a, state the value of the constant aaa.
(ii) Write down an equation for another single transformation of CCC that also passes through the origin.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions 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), matched to the AQA A Level Maths (7357) 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.
