It is "D"! Really?

Had an interesting conversation after a test yesterday.

We teach parent functions ... and the current one is the absolute value function.

There were several questions on the test that stumped students but this one I just don't understand.

So we practice ... show me the absolute value parent function with your arms. Is the absolute value PARENT function ever negative ... no! What is it's equation ... yes ... always y = |x|. What if I reflect the graph ... what is the parent function? The parent function is always positive, it's always y =|x|.

Enter test question:
What is the parent function that represents the data below?

Yes ... a few of our questions are multiple choice. They are rare but we do it to model other standardized testing.

I haven't actually counted the test papers ... but close to half of the students chose D.

So ... a young man finished his test and was getting ready to leave class. He said he was sure he did well and he typically does quite well.

I was curious though how this one question went ... so I said ... tell me again about the parent function? He laughed ... ma'am it is always positive!

Super, I said, and showed him a Desmos graph of the points above. Tell me then ... what is the parent function for this set of data? What answer did you choose?

Ummmm ... D!

Really!?! the parent function is always positive?

The teenage brain ... who can say?