Chapter 31: Translation of Functions: Situation 25 From the MACMTL-CPTM Situations Project

During a unit on functions, the translation of functions was discussed. When the class encountered the function y = (x – 2)² + 3, one student noted that the vertical translation of 3 upward makes sense when compared to the +3, but the horizontal translation of 2 to the right does not make sense when compared to the -2 in the function rule.

Focus 1 and Focus 2 use a quadratic function as the original function for conve- nience and because it was the function type speci?ed in the Prompt. One may translate any function similarly. Throughout this situation, the term parent function is used to refer to functions such as f (x ) = x², g (x ) = x³, h (x ) = cos(x ), and the term child function is used to refer to a transformation, in particular a translation, of a parent function (such as f 1(x ) = x² + 3, g 1(x ) = (x – 1)³, and $h1(x)=cos(x+p2)-4$ In general, the Foci address the relationship between f (x ) and f (x – h ) + k.