The intensity of radiation L L \,L at a distance d d \,d from a specific energy source is modeled by the function L(d)=1d4\displaystyle L(d) = \frac{1}{d^4}L(d)=d41 for d>0d > 0d>0.
Sketch the graph of L(d)L(d)L(d) for all d≠0d \neq 0d=0, clearly indicating the equations of any asymptotes.
A revised model for a shielded source is given by M(d)=1256d4\displaystyle M(d) = \frac{1}{256d^4}M(d)=256d41. The graph of L(d)L(d)L(d) can be transformed into the graph of M(d)M(d)M(d) using a single stretch parallel to one of the coordinate axes.
Student A claims that the required transformation is a stretch parallel to the LLL-axis. Student B claims that the required transformation is a stretch parallel to the ddd-axis.
Determine, providing mathematical justification, whether Student A is correct, Student B is correct, both are correct, or neither is correct.
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.