tag:blogger.com,1999:blog-1210764468738959445.post8879520471263886932..comments2017-08-29T18:37:30.314-04:00Comments on Do we understand?: Transformations vs. Order of OperationsProfJonhhttp://www.blogger.com/profile/10458868925258435912noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-1210764468738959445.post-46993278319786353262017-08-29T18:37:30.314-04:002017-08-29T18:37:30.314-04:00Thanks Kim. I think your example also "follow...Thanks Kim. I think your example also "follows the order of operations" in the sense that I was referring to on Nov. 4. That is, when we *evaluate* the function for a specific value of x, we must either multiply by -2 then subtract 4, or (equivalently, as you point out) add 2 and then multiply by -2. THEN we may apply the square root to get the final result.<br /><br />What I think you are pointing out is the fact that the 'rules' given in the book don't work "on the inside". In fact, they seem to work backwards: the compression (toward the y-axis) has to be applied before the shift (weird), and the shift goes the 'wrong' way ($**!). <br /><br />I wouldn't label that a problem with the order of operations, but with the order of applying function transformations. The order of applying transformations that was given in the textbook doesn't work, because it doesn't apply. Your example has a coefficient on x other than 1, and the textbook's scenario [a*f(x+h)+k] excludes that case.ProfJonhhttps://www.blogger.com/profile/10458868925258435912noreply@blogger.comtag:blogger.com,1999:blog-1210764468738959445.post-67220718224184966412017-08-12T14:13:23.052-04:002017-08-12T14:13:23.052-04:00To me, the inside is the opposite of the order of ...To me, the inside is the opposite of the order of operations. It's hard to see with a coefficient of -1. So consider sqrt(-2x-4). To get the transformed graph from the parent, there is a horizontal shrink by a factor of 2 and a reflection across the y-axis, and a horizontal shift of 2 to the left...to see it, you have to write the expression sqrt(-2(x+2)). The order of operations would then indicate the "adding two" first due to the grouping symbol, but in fact the shrink and reflection indicated by the multiplication must be done first. (Also, the subtraction of -1 in the above example should indicate a more the the RIGHT, but the move is actually to the left, so it should be factored first to avoid confusion.)<br />Kim Collierhttps://www.blogger.com/profile/09825215869992200246noreply@blogger.comtag:blogger.com,1999:blog-1210764468738959445.post-72353883262645350982016-11-04T17:25:11.828-04:002016-11-04T17:25:11.828-04:00Nice question! It certainly follows order of opera...Nice question! It certainly follows order of operations--has to, right? <br /><br />x --> (-x) --> (-x)-1 --> sqrt((-x)-1)<br /><br />First work within the grouping symbol (sqrt). Then multiply x by -1. Then subtract. Now that's done, so look outside the grouping symbol. That means apply the sqrt.<br /> <br />But the question is whether the "rules" provided by the book will yield the same result as applying the order of operations. The answer there is no, but that's ok: the conditions for applying the rules has not been met: the function is you named has a horizontal reflection (b/c of the -x), and the book's "rules" are not meant to be applied in that case. Jon Hasenbankhttps://www.blogger.com/profile/10538045353594459444noreply@blogger.comtag:blogger.com,1999:blog-1210764468738959445.post-6722337669047015762016-11-04T13:33:17.026-04:002016-11-04T13:33:17.026-04:00What if you graph Square root of (-x-2)? Does this...What if you graph Square root of (-x-2)? Does this follow order of operations? Unknownhttps://www.blogger.com/profile/15940809643983289059noreply@blogger.comtag:blogger.com,1999:blog-1210764468738959445.post-6982269408017197092016-02-02T21:15:56.330-05:002016-02-02T21:15:56.330-05:00I meant GEMA instead of PEMDAS--not order of opera...I meant GEMA instead of PEMDAS--not order of operations! LD Helferhttps://www.blogger.com/profile/15362613994636151867noreply@blogger.comtag:blogger.com,1999:blog-1210764468738959445.post-47052729657748791762016-02-02T07:53:38.041-05:002016-02-02T07:53:38.041-05:00Thank you for linking to my blog post on using GEM...Thank you for linking to my blog post on using GEMA instead of order of operations. I have received great feedback from teachers who have tried using this method instead of PEMDAS. <br /><br />Lauren @ www.leafandstemlearning.comLD Helferhttps://www.blogger.com/profile/15362613994636151867noreply@blogger.com