\input zb-basic \input zb-matheduc \iteman{ZMATH 1996a.00471} \itemau{Ligh, S.; Wills, R.} \itemti{On linear functions II.} \itemso{Math. Comput. Educ. 29, No. 1, 32-52 (1995).} \itemab 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.) \itemrv{~} \itemcc{G74} \itemut{} \itemli{} \end