tag:blogger.com,1999:blog-6651514617266100245.post4876472058185297326..comments2024-01-03T04:58:04.221-05:00Comments on I Hope This Old Train Breaks Down...: Function Transformations Nitty GrittiesUnknownnoreply@blogger.comBlogger11125tag:blogger.com,1999:blog-6651514617266100245.post-79708407406681039902014-04-12T22:40:25.034-04:002014-04-12T22:40:25.034-04:00This is a fantastic explanation! I really like it!...This is a fantastic explanation! I really like it! Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-15680198743828947662012-02-07T00:00:08.068-05:002012-02-07T00:00:08.068-05:00Hi Jessie,
It worked ok for me but not great. Thi...Hi Jessie,<br /><br />It worked ok for me but not great. This year the curriculum is different so I cannot really say if there is one thing I am changing, but my colleague says that she finds it much easier to first teach quadratic transformation, then sinusoidal transformation, then general transformation. Move from concrete to abstract helps the kids understand.<br /><br />Mimiuntilnextstophttps://www.blogger.com/profile/15285583728476473117noreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-67175445329731377062012-02-06T23:47:31.631-05:002012-02-06T23:47:31.631-05:00Hi there,
I am teaching transformations in algebra...Hi there,<br />I am teaching transformations in algebra 2 and I came across your blog in my research. It's almost a year later, did you find this technique worked well? What are you doing differently this year? My kids are really struggling with these (and so have past students) so it's my goal to find some good techniques on this!<br />JessieJessienoreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-72586170754008343912011-02-13T13:26:19.071-05:002011-02-13T13:26:19.071-05:00I like the idea of the axes being stretched/squish...I like the idea of the axes being stretched/squished/translated. I'm going to use it. Thanks!untilnextstophttps://www.blogger.com/profile/15285583728476473117noreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-89930866962866248192011-02-13T12:19:18.777-05:002011-02-13T12:19:18.777-05:00Notice that @glsr's system works for stretches...Notice that @glsr's system works for stretches and squishes as well. <br /><br />y = sin( x/3 ) is a STRETCH in x<br /><br />y = 3 sin(x) ---> (y/3) = sin(x) <br /><br />this is a STRETCH in y.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-28444559595373168562011-02-07T23:39:24.226-05:002011-02-07T23:39:24.226-05:00One of the ways that I attack the problem of movin...One of the ways that I attack the problem of moving in the opposite direction is to describe the transformation as happening not to the graph, but rather to the axes. So, for example, y = (x-2)^2 will mean graph x^2 but shift the axes to the left by 2. Of course, one might counter that now the vertical shifts are moving in the wrong direction, but this is only because we choose to put the shift on the wrong side. For instance, y = x^2 + 2 could be written as y - 2 = x^2 and then it all makes sense: graph x^2 and move the axes down 2.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-35011939336391015062011-02-07T01:23:20.626-05:002011-02-07T01:23:20.626-05:00Whipping up a quick GeoGebra applet with adjustabl...Whipping up a quick GeoGebra applet with adjustable transformation parameters really brings it alive for some students.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-16413695670950506182011-02-06T16:27:18.680-05:002011-02-06T16:27:18.680-05:00@Mr. H: thanks! I've definitely spent a good w...@Mr. H: thanks! I've definitely spent a good while carefully poring over those handouts yesterday before writing my lesson. I liked his approach of making kids plot each sub-transformation one at a time. It's a good in-class practice sort of thing once kids have a basic grasp of the patterns, but I wanted the exploration part to be computer-based, so I ended up whipping up my own version instead of just using his.<br /><br />My kids are also not starting completely from scratch with this material. They already can efficiently graph things like <br />f(x) = -3(x - 2)^2 - 6 using transformational ideas a la what Meg described above, so making the exploratory part on the computer has the added benefit of speeding along the concept-building.<br /><br />@Meg Sam Shah's worksheets (see Mr. H's link above) use the same method of factoring to "make it pretty" as you suggest. But, how do you explain to your kids why we "do the opposite" on the inside, and why it's necessary to "make it pretty"? That's part of what I've always struggled with. <br /><br />@Paul Got it. Thanks for looking out. Rational functions are tricky because it's the only one where kids can't think in terms of what's "inside" vs. "outside"... Think that's the one where the understanding of order of ops will really come into play.untilnextstophttps://www.blogger.com/profile/15285583728476473117noreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-33301955598385219622011-02-06T15:19:09.219-05:002011-02-06T15:19:09.219-05:00Sam has nice sequence for this topic with very det...Sam has nice sequence for this topic with very detailed worksheets/notes. It might give you some ideas.<br /><br /><a href="http://samjshah.com/2009/04/23/function-transformations-2/" rel="nofollow">http://samjshah.com/2009/04/23/function-transformations-2/</a>Mr. Hhttps://www.blogger.com/profile/12620847580362451503noreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-31436231212861343372011-02-06T12:20:57.573-05:002011-02-06T12:20:57.573-05:00This looks really good and the combination of expl...This looks really good and the combination of explanatory notes and an exploratory activity should help to lock in the learning. <br /><br />One minor hiccup came to mind: some students could get momentarily lost with h(x) and may need to see it re-written as <br /><br />h(x) = <br /><br />4*( 1 ) - 2 <br /> (------)<br /> (-5x+1 )<br /><br />http://www.wolframalpha.com/input/?i=h%28x%29%3D4*%281%2F%28-5x%2B1%29%29-2<br /><br />to be able to successfully apply the PEMDAS model you’ve built for them. But I think that that is why h(x) is a great example to include in the lesson.?https://www.blogger.com/profile/09000980455095316183noreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-34083931356550752832011-02-06T12:19:12.306-05:002011-02-06T12:19:12.306-05:00In Alg II, I teach almost all graphing as graping ...In Alg II, I teach almost all graphing as graping by translating, and they learn "what is inside changes signs, what is outside stays the same." So if you have y = (x - 2)^2 + 3, you know your new origin will be at (2, 3). Want to throw in y = 3(x - 2)^2 + 3? Well, that makes the parent graph y = 3x^2. So take your original t-chart {(-2, 4)(-1, 1)(0,0)(1, 1)(2,4)} and multiply all the y's by 3 and graph these points from your new "origin." Want to get really crazy? (and I mostly leave this for trig) y = 3(2x-2)^2 + 3. Make it look pretty: y = 3(2(x-1))^2 + 3. Find the vertex: (1, 2). Find your parent: y = 3(2x)^2. Multiply the y's of the original by 3. Since 2 is inside the parenthesis, do the opposite--divide your x values by 2. So now you have (-1, 12) (-.5, 3)(0,0) (.5, 3), (1, 12) that you will translate to (1, 2).<br /><br />Maybe it seems like "just a bunch of blind rules" but we discuss the "why" when we first introduce it (with absolute value), then after that it's a piece o' cake.Meghttps://www.blogger.com/profile/08395474750276931370noreply@blogger.com