Friday, May 28, 2010

Does This Make Sense To Anyone Else?

I'm reviewing the actual unit tests completed by one of my high school students right now, in order to be able to make up Practice Sheets for the student that reflect what was previously tested as well as focus on whichever areas the student was weakest in. This is all in preparation for the final exam, late next month.

The first thing I noticed is just how full of errors the tests have been. Usually it's just poorly worded sentences in which you can fairly easily guess which word was left out or what wrong word was used. But the following question absolutely stumped me (as to its meaning) when I first read it over:

If f(x) = 3x - 4 and g(x) = 2(x - 1) + 3, find the value of x.

To my understanding of function notation, this makes no sense whatsoever. The values (plural) of x for each function, otherwise known as the function's domain, are whatever subset of the set of real numbers that you can legitimately substitute into each function wherever x appears. (In this case, the domain would be all real numbers.) Therefore asking what the value (singular) of x is seems ludicrous.

After thinking about it for a minute or two, I decided that they probably meant to ask "... find the value of x where f(x) = g(x)" but there's no indication of that in the question itself. I can see that a value of 5 for x would yield the same answer for the two functions: f(5) = 11 = g(5). But who knows if that's what was even meant, when the question is so ambiguously worded. (My student had no idea at all, and got 0 on this particular part of the test.)

I'm starting to wonder about the standards being applied to some of these courses.

3 comments:

Anonymous said...

There is no equation to solve there. f(x) and g(x) are function definitions. There is no question being asked. It's like saying, "Here's an apple. Here's an orange. Find a banana."

Finding the value of x is a non sequitur.

If that question were part of a test then it should be discounted.

Kimota94 aka Matt aka AgileMan said...

That was my reaction, as well. And yes, it was part of a test... and no, it wasn't discounted, as far as I can tell.

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