Date: Nov 16, 2012 11:32 PM
Author: Clyde Greeno @ MALEI
Subject: Re: Problem with transformations
Apart from Larson's apparent fetish with useless equations ...

This is one of those times when the most effective approach is to NOT try to

*tell* anything, until the students have an under-standing of what you are

talking about. Let them graph a few cases from the (x-h)^2 family ... the

a(x-h)^2 family ... the (x-h)^2+k family .... and the a(x-h)^2+k family ...

and THEN talk about the whats, whys, and whethers (or not the curves reach

certain values).

- --------------------------------------------------

From: "Peter Duveen" <pduveen@yahoo.com>

Sent: Friday, November 16, 2012 6:38 PM

To: <math-teach@mathforum.org>

Subject: Problem with transformations

> The text (Precalculus with limits: a graphing approach Larson, etc.) tells

> us as follows (p43):

> "...you can obtain the graph of g(x) = (x - 2)^2 by shifting the graph of

> f(x) = x^2 two units to the right, as shown in Figure 1.42 [AN ASSERTION].

> In this case, the functions g and f have the following relationship.

>

> g(x) = (x - 2)^2

>

> = f(x - 2) (right shift of two units)[AN ASSERTION]

>

> The following list summarizes vertical and horizontal shifts:" etc. etc.

>

> I feel the assertions are not self-evident, and the treatment is generally

> confusing.

>

> I would have treated this differently. I would have first attempted to

> establish a relationship between a function and another function which is

> the translation of the first so many spaces horizontally.

>

> The relationship is f(x) = g (x + c). That is, the two functions have the

> same value when the arguments of f and g differ by a particular constant.

> Assuming we know the form of f(x), what is the form of g(x)?

>

> We introduce the argument f(x - c), and want to see what happens to g,

> namely, f(x - c) = g[(x - c) + c]

>

> We thus arrive at the expression f(x - c) = g(x). We have now established

> the form of g(x) in terms of f(x), which we know. It is simply f(x - c),

> which is not the same as f(x). In other words, we have derived and

> demonstrated what the textbook merely asserts.