Just in case anybody got the wrong impression and hoped or feared we’d turned over a new leaf, we’ll be posting a number of WitCHes in the next few days. We’ve finally had a chance to look at the 2021 NHT exams (although the exam reports have still not appeared). As usual, the exams are clunky and eccentric, and we’ll be posting a brief question-by-question overview of the exams. But, first, some highlights.
The following question is from the 2021 NHT Methods Exam 2. It seems to us more of a PoSWW than a WitCH, but we have seen the exact same issue arise in a recent SAC. So, presumably, this issue is more widely spread.
As commenters have pointed out, none of the options are correct. A function f is defined to be strictly decreasing on its domain if f(b) < f(a) whenever b > a, and this is false for all the given restricted domains. It is also standard in VCE to only apply the definition on intervals, which also kills options A, D and E. (There is no problem applying the definition on more general domains but, for the first reason given, this does not save the question.)
There is also a “local” notion of decreasing function. So, for example, one might describe a function as decreasing at x = -4, indicated, say, by the derivative at that point. But, as illustrated by the failure of option D, the global definition does not equal the sum of the local notions.
UPDATE (22/09/21) Surprising no one, the examination report simply pretends that VCAA didn’t screw up, and gives the answer as D.