Bob Lochel writes:

“I used this question as part of a benchmark assessment given to over 1,100 students at our high school, as preparation for the state test. Only 14% of students gave the correct answer B, while 66% of students chose A as their response. I’m not surprised that students would perform weakly on a domain/range question, but I am surprised that so many chose A. I featured this problem as a set-up for a domain and range activity on my blog: http://mathcoachblog.wordpress.com/2013/01/22/home-on-the-range-and-the-domain/, but feel free to share it with the mathmistakes crowd.”

So, what do we think about choosing A? Any theories?

## 6 replies on “Range of a Function”

There’s a dot placed by every y-value of the options, except for 0. If students don’t know the difference between filled and unfilled plotted points, then maybe they want for the one with no points at all?

I have no doubt that most students struggle with domain and range, but wonder if the question is just a bit mean-spirited. It’s not incorrrect in any way, but you need to focus your eyes on the bottom-left of the graph to find the zero, rather than honing in on where the “action” of this graph seems to be. But looking forward to hearing all o your thoughts!

Along the same line of thinking: if the students were unsure of what to do, and the number “0” pops up as an answer choice, it might be easy for them to make the leap that “0” means the origin/(0,0). The origin doesn’t have any part of the function’s graph close to it, therefore the origin must not be in the range, therefore “0” is not in the range.

It also has the added bonus of being the first answer choice on a tricky problem, so students might be tempted to just go with it and move on to something they might be more comfortable with.

I might find it a little more convincing if at least the tic marks showed 1,3,5, etc. As a student, I am not sure that the blob is at exactly 3. And then I’m stuck with assuming I am wrong, and use the x values, which has me picking (0,0) out of desperation.

In every day language, range usually just means from the least to the greatest. So in everyday language, 0 is the closest to not being in the range – the other values are clearly between the least & greatest values. I wonder if it would affect the answers if you moved the point (-8,0) to (-8,3), so that the x-intercept is in the “middle” of the graph. I also wonder if removing the grid, to make the jumps more obvious, would affect the answers.

Maybe it has something to do with that they would think the entire graph is above the x-axis?