I’m returning to a theme from an earlier post, misreading of instructions on quizzes and exams. This week’s quiz in my precalculus class included the following question.
Q1. Create a piecewise function that represents the graph shown below. Assume the pieces of the graph are built from the functions listed below, with appropriate transformations:
y = x
y = x^2
y = ln(x)
The graph shows a continuous, piecewise function from 0 to 3 that was build from three joined segments of subfunctions,
y = x from 0<=x<=1
y = (x-2)^2 from 1<x<2
y = ln (x-1) from 2<=x<=3
Those three lines are, essentially, the answer I was looking for.
Most of the students answered the question with transformations, not always correct transformations, but in the spirit of my intention. About 1/3 of the students, however, answered as follows (some with mistakes in the inequalities, but let’s ignore that),
y = x from 0=<x<=1
y = x^2 from 1<x<2
y= ln (x) from 2<=x<=3
From the reading of the instructions, they seemed to have assumed that ‘with appropriate transformations’ meant that the transformations did not need to be shown in the list of piecewise functions. Apparently they thought that I was testing for the correct partitioning of the domain, and that I didn’t really care about an accurate representation of the graph for each partition. Since more than just one or two students chose this interpretation, I am wondering if perhaps the question is indeed ambiguous. Therefore, I have a question to those of you who feel that you can put aside what I’ve already explained and can read the question as if you were taking the quiz along with my students. Do you believe that the question, as worded, is ambiguous and might have misled you into replying without transformations? Do you have any suggestions for a better re-wording of the question? Comments at all?