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.
281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.