@article {MATHEDUC.02310460,
author = {Ligh, S. and Wills, R.},
title = {On linear functions II.},
year = {1995},
journal = {Mathematics and Computer Education},
volume = {29},
number = {1},
issn = {0730-8639},
pages = {32-52},
publisher = {MATYC Journal, Old Bethpage, NY},
abstract = {Let L(R) be the set of linear functions defined over the real number R. Once we have characterized the subset of L($\bbfR$) corresponding to the subset of $\bbfR{}^2$ generated by a function y = f(x) to be the set of lines tangent to the graph of y = g($\chi$) we will show how to use this result to obtain a whole family of related results. We do this by demonstrating what effect translations and dilations of the function y = f($\chi$) have on the function y = g($\chi$). It can be shown that any quadratic function can be expressed in terms of translations and dilations of y = $\chi{}^2$, the upper and lower halves of any non-rotated ellipse can be expressed in terms of translations and dilations of y = $\sqrt{1-\chi{}^2}$, and the branches of any nonrotated hyperbola can be expressed as translations and dilations of either y = $\sqrt{1+\chi{}^2}$ or y = $\sqrt{\chi{}^2-1}$. Thus, our theorem will enable us to characterize the subsets of L($\bbfR$) corresponding to the subsets of $\bbfR{}^2$ generated by functions whose graphs are conic sections by knowing the subsets of L($\bbfR$) corresponding to the subsets of $\bbfR{}^2$ generated by the four functions y = $\chi{}^2$, y = $\sqrt{1-\chi{}^2}$, y = $\sqrt{1+\chi{}^2}$, and y = $\sqrt{\chi{}^2-1}$. The software package Maple is used to illustrate some examples. (orig.)},
msc2010 = {G74xx},
identifier = {1996a.00471},
}