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.
33 exam-style questions on OCR (MEI) A Level Maths 1.4 Graphs, covering 1.4.1 Graphs of functions, 1.4.2 Intersection points with axes, 1.4.3 Completing the square for a quadratic curve, 1.4.4 Sketch graphs of simple functions, 1.4.5 Stationary points when curve sketching, 1.4.6 Graphs of reciprocal-type functions, 1.4.7 Single transformations of graphs, 1.4.8 Combined transformations of graphs (A-level only), and 1.4.9 Stationary points of inflection (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.