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Topic: Algebra 2/Trig Regents
Replies: 55   Last Post: Jul 1, 2011 6:01 PM

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 ElizWaite@aol.com Posts: 543 Registered: 12/3/04
Re: Algebra 2/Trig Regents
Posted: Jun 21, 2011 11:31 PM
 att1.html (3.5 K)

Doesn't the school principal have the right to allow teachers to use their best judgement? In other words, if the teachers explain to the principal that question 32 is flawed and that the teachers would like to award full credit for various answers based on that, can't the principal give his/her permission?
I'm pretty sure they can
Liz Waite

-----Original Message-----
From: Nick B <nbianculli@gmail.com>
To: nyshsmath <nyshsmath@mathforum.org>
Sent: Tue, Jun 21, 2011 10:18 pm
Subject: Re: Algebra 2/Trig Regents

She's correct in saying that the inverse relation of a function may not be a
unction itself. Every function has a corresponding inverse relation; however,
e usually say a function is invertible iff its inverse relation is a function.
owever, the question specifically asked to find f^-1(x), which implies that the
nverse relation is a function. After all, the letter f stands for function and
ny good book will define the notation f^-1 to stand for the inverse function of
. So for the question to ask for an inverse function of f(x) = x^2 - 6 requires
domain restriction. If the question asked to find the inverse, then I could
ee her point but since the question specifically used the notation f^-1(x), I
ompletely agree with you.
In higher mathematics, there are such objects called multivalued functions, but
e certainly don't study these concepts in any detail in high school.
The following Wikipedia article does the topic justice, and introduces
ulti-valued inverses:
http://en.wikipedia.org/wiki/Inverse_function
It's the same concept in question 19. y = cos^-1(x) denotes the inverse cosine
UNCTION, which is the inverse of y = cos x restricted to a domain of [0, pi].
What's sad is that we're the concerned, diligent math teachers who want to get
t right and you bring a legitimate concern to light and are told that you won't
win the argument". At the minimum the question is ambiguous and poorly posed,
egardless of whether SED thinks you didn't win the argument. What's even sadder
s that this test is supposedly reviewed by trained eyes. How are
athematically educated people not picking up on these glaring errors and
mbiguities? I saw the ambiguities within seconds of reading the questions (as
'm sure most all of us did) and somehow those questions ended up on the test.
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