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.
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.