# Sam Standard Essay

545 Words3 Pages
Standard Function Form All graphs of functions belong to a family of like curves, whether they be polynomials like cubics and quadratics, sine waves, exponentials, hyperbolas, etc…. Accordingly, graph sketching begins with an understanding of what its most basic member looks like. From this knowledge, all other members of that family are derived via an appropriate sequence of transformations. The issue becomes; how can you identify such a sequence and then apply it consecutively to the curve in question. One approach is to place the function into Standard Function Form, if not already. That is, transcribe it into the form: This gives immediate access to a valid sequence of transformations from the more basic rule, . This sequence is affectionately known as “Dr T” – indicating the order in which the identified translations are to be applied; Dilations, Reflections and, lastly, Translations. However, it should be noted that the order in which dilations and reflections are applied is interchangeable. The only important positioning in the sequence are the Translations, which must always come last! Describe a sequence of transformations that enables to be transformed into . | Method1: Function level understanding and the Standard Function Form. Step 1 Place the given function into Standard Function Form Step 2 Identify a sequence of transformations, ensuring that the translations come last. | Sequence * Reflected about the x-axis. * Dilated by 2 from the x-axis (in the y-direction). * Reflected about the y-axis. * Dilated by from the y-axis. * Translated units to the right (in the positive x-direction) * Translated 5 units up (in the positive y-direction) | Have a go at identifying a valid sequence of transformations that transforms the rule into . And hence sketch the function. Note: This transformed