Chapter 1.5 – Graphical Transformations

Assessment

On day #11

• • 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)

1-5 Function Translations

Watch before Day #12 lesson

1-5 Exploring how changing the parameters of y = ax2 + bx + c affects the graph

Optional: explore before/after Day #12

1-5 Order of Function Transformations

Optional: Watch before/after Day #12 lesson

1-5 Exploring transformation of the basic f(x) graphs

Optional: explore before/after Day #12

1-5 Function Transformations for "Baby Batman Equation"

Watch before Day #13 lesson

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.

1-5 ADVANCED Function Transformations for "Baby Batman Equation"

OPTIONAL: Watch before/after Day #13 lesson

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.

More Transformation Practice

• • TransformationExercises_extra.pdf

  • TransformationExercises_extra2.pdf

  • transformation_exercises_examQ1_handout.pdf (to be passed out in class)

Study guide and practice test for Chapter 1.5 Assessment

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.

Hanging Beads with Geogebra

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.

Here's the activity in GeoGebra, allowing the user to simply drag a point in the plane to adjust pre-entered equations.

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 Graphs

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

Go to next page, Chapter 4.1.