kitchen table math, the sequel: Regents inverse function question

## Wednesday, June 22, 2011

### Regents inverse function question

Grace said...

I have no confidence in New York State’s ability to create a good test of mathematics, at any level.

Double whammy - state tests are used to assess students AND to evaluate teachers. What a mess.

Hainish said...

Grace, NY State's High school level science assessments are created BY teachers, giving a slightly different meaning to "AND evaluate the teachers."

I'm not sure if it's also the case for math.

Anonymous said...

Hainish,

teachers are involved in every step of creating the exams, but they do not actually create them. What?

The look of the exam is set by a company in consultation with NYSED. The creation of the exam is broken into lots of small tasks, and those tasks are performed, mostly, by teachers. But teachers do not have control of the overall feel or any other aspect of the end product.

Jonathan

rocky said...

I thought an inverse was just the reflection about the line y=x, so the inverse of y=x²-6 would be y=±sqrt(x+6)

The question didn't say the inverse had to be a function; it's just a parabola that opens to the right. If you forget to mention the "-", you lose the lower "arm" because the sqrt function only gives you the positive square root.

Anonymous said...

Rocky,

that f^(-1)(x) notation is functional notation. There's no easy way around that.

We conventionally teach inverses AS inverse functions, and some of us actually teach kids to restrict the domain of a function so that it will have an inverse (not so that the inverse is a function, the difference in language is important)

It is not until analysis that we begin to reexamine the non-functional relation (or in plainer image, the preimage) that you are thinking of.

Reflecting the graph is a shortcut to finding the inverse, but only if the original function is 1-1.

Jonathan

rocky said...

I betcha that's why the example answer only got one point out of two. It didn't have the ±

Even functions: f(-x)=f(x)
Odd functions: f(-x)=-f(x)

"Self inverse" relations: f(f(x))=x