Describing and Understanding the Transformations of Functions | A1 & 2

Looking for a comprehensive, editable resource to teach your students or child about function transformations, including shifts left/right, down/up, vertical stretch/shrink, and x-axis reflections? (Note: no horizontal stretches/shrikes or y-axis reflections in this lesson.) This set of lesson notes, extra practice (homework) worksheet, and exit ticket to check understanding of the lesson is excellent in helping students achieve mastery of this objective.

Students will be given the opportunity to do some exploratory learning through Desmos activities (linked in notes; optional) to start seeing how changing the equation of a function changes its graph. Notes will then dive into what aspects of a function cause which rigid and non-rigid shifts. Practice identifying shifts and sketching resultant graphs is provided. This lesson is a great one in the beginning of the year as it also exposes students to different function families that they might be learning about throughout the year.

Objective(s):

By the end of this lesson, students will be able to describe what affects changing different features of a function (a, h, & k) in a*f(x-h)+k does to the graph of that function.

What's Included:

• Cover Page: includes link to editable google doc

• Notes: 4 pages + answer key

• Extra Practice: 2 pages + answer key

• Exit Ticket: Three identical exit tickets are included (this is meant to be cut in thirds to save paper) + answer key

Editable Format:

• The lesson file includes both a printable pdf version and a link to make a digital copy of the original google doc. As a google doc, all text is editable. Graphs are NOT editable, but can be replaced with your own.

Random Tidbits:

• My students were a lot more engaged in this lesson after a chance to do the Desmos actives. Having a few minutes to explore/play with the math made them more bought in and curious as to the specifics of what each aspect of a function does to the graph of the function. This is obviously optional, but could be done individually or together as a class. Getting students to be wondering, "why does changing [this] do [that]?" would be such a win and make this concept more likely to stick in their brains.

• One of the things that I thought to do on each exit ticket that is super simple, but paid off huge dividends relationally with my students, is adding a sentence stem along with asking for their names. 1) Students almost never forgot to write their names on the exit ticket. 2) Daily, students would leave chatting with each other about what they wrote to answer the sentence stem. 3) It gave me something personal to chat with students about the next day as they entered class or I passed back exit tickets and helped me get to know them. 4) Even if students struggled on the exit ticket, I noticed that they never seemed to leave class feeling down or defeated because they could always at least answer the prompt about themselves.

Supports CCSS math standards for Algebra 1 & 2. Thank you!