Objectives (click/tap to expand)
Perform and describe graphical transformations
Find equations of reflections
Analyze transformations
free response
1 sheet, front and back
Old Stuff: domain, range, continuity, incr/decr/constant, symmetry, boundedness, extrema, asymptotes, end behavior
New Stuff:
combining functions: f+g, f-g, f*g, f/g, f(g(x)) or fog
parabolas: standard form vs. vertex form
Transformations: translate, stretch/shrink, reflect (see handouts)
Explore this Geogebra file to see how varying the parameters of a quadratic function in "standard form" affects the graph. I think you'll be surprised by what you see.
The unexpected behavior helps us appreciate why "vertex form" of a quadratic function is preferable for some purposes.
This is probably the first day that we've discussed Stretches/Shrinks in detail. Look over textbook p137 before viewing this video. Hopefully you'll start to get the hang of it by the end. Here's the "Examples" handout from class with my solutions on the second page. Here is the "Homework" handout as well.
Explore this Geogebra file to see how varying the various parameters of any "basic" function affects the graph.
This video is admittedly long. If you choose to watch it, your reward for learning the content within it is a full block to work on the assignment during our next class meeting. If you don't watch it, I'll teach the content in class but you'll have little/no time to work on assignment in class.
A web search yields plenty about the "Batman Equation" which went viral in 2011 (amongst nerdy circles, at least).
For my super-nerds, remember to check out the very cool online graphing calculator or app from Desmos.com, and the graphing challenges at DailyDesmos.com.
Here is the assignment handout if for whatever reason you didn't get it in class.
If you have a newer TI-84 Plus CE calculator, you may be able to avoid the hacky way of restricting the domain shown in this video. Press the Math button, and near the bottom of the list you may see the option B:piecewise. If so, make a 1-piece piecewise function. See if you can figure out how on your own, or see here for a quick explanation.
This video is optional, so let's see where ma real Nerds at. If you really get into this stuff (using function transformations to create designs), then here are some "advanced" techniques.
Includes: Graphing semicircles, using absolute value to make a function symmetric about the y-axis, using {curly braces} to graph a family of functions with just one equation, and how to save your graph as a program.
You'll see how the nine function equations from the earlier Baby Batman video can now be consolidated into just two equations! If you're really hard core, you may even see how to get it down to a single equation in your calculator.
transformation_exercises_examQ1_handout.pdf (to be passed out in class)
Here's my poem/animation related to graphical transformations. By now all the mathematical references should make sense!
If you're looking for an even greater challenge, check out my own series of function transformations which display pictures when graphed. These are the images shown very briefly at the beginning of the video. In many of them I use a few types of functions that are not part of your "basic" collection, and I also use a calculator trick or two that is not shown in the video. Perhaps you can figure out how they work on your own, but please ask if you get stuck.
Now go make some of your own!
Finally, here's another video giving a little insight into the making of the original batman equation. Unlike your teacher, this guy has a frikkin' adorable British accent.
Umm, here's somewhat of a study guide. Don't say I never gave you nuthin.'
Here is a screen-capture of the slide I showed in class with the suggested practice test exercises.
In this activity you will use your abilities to transform basic functions in order to find the equation that models the shape of a string of Mardi Gras beads suspended from both ends.
Or if you're feeling adventurous, start from scratch with a new Geogebra file. You may click on any of the images below to get the full photo in higher resolution.
Or for the truly adventurous, hang your own beads and take your own photo to use in a new Geogebra file.
Here's the activity in GeoGebra, requiring the user to enter/edit the equations from scratch.
If we're using Desmos for this activity, click on the link below the image you want to use. Image resolution is low in Desmos versions, but it's good enough for this activity.
The "don't use" links are accessible, but they don't support the intent of the lesson very well.
If it enters the discussion, here's a Desmos graph including a photo of the St. Louis Gateway Arch.
Desmos: Beads06
Desmos: Beads07
Desmos: Beads08
Desmos: don't use Beads09
(too far off center)
Desmos: Beads10
Desmos: Beads21
Desmos: Beads22
Desmos: Beads23
Desmos: Beads24
Desmos: don't use Beads25
(equation too "basic")
I was very impressed with students' creations using their knowledge of graphical transformations on Desmos.com in class recently. Students deserve to be proud of how wonderfully these turned out.
Desmos Graphs 2024-25 screen captures and photo of wall display outside Mr. W's classroom
Desmos Graphs from previous years (click/tap to expand list)
Desmos Graphs 2023-24 screen captures and photo of wall display
Desmos Graphs 2022-23 screen captures and photo of wall display
Desmos Graphs 2021-22 screen captures and photo of wall display
Desmos Graphs 2020-21 screen captures and photo of wall display
Go to next page, Chapter 4.1.