Algebra 2 unit 5 lesson 1 homework answers

Middle School / Math / Algebra

emathinstruction

Oct 7, 2016

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Algebra

In this lesson we review much of the material from Common Core Algebra I sequences, including notation and sequences that are defined recursively.

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Alg2.5 Transformations of Functions

In this unit, students consider functions as a whole and understand how they can be transformed to fit the needs of a situation, which is an aspect of modeling with mathematics (MP4). Students make connections between representations as they translate, reflect, and apply scale factors to different types of functions. As the unit progresses, so too does the language students use to describe transformations with precision (MP6). The unit ends with students applying transformations to different functions to model a real world data set.

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Lessons

Translations, Reflections, and Symmetry

Scaling Outputs and Inputs

Putting It All Together

The purpose of this lesson is to introduce students to one of the big ideas of the unit: we can transform functions to model sets of data. The main focus of this lesson is to elicit ideas and language around transforming graphs that will be refined throughout the unit. Later in the unit, students will make connections between graphical and algebraic transformations and directly manipulate equations to transform graphs.

The two functions in Which Function? are both good fits for the data, providing students with the opportunity to make an argument about why a particular function is a better fit (MP3). Students continue to critique each other's arguments as they make adjustments to the functions to get a better fit. In the next activity students take turns describing transformations between pairs of graphs, giving an opportunity for students to refine their language and connect back to transformation vocabulary from geometry (MP6).

One of the activities in this lesson works best when each student has access to devices that can run the digital applet because students will benefit from seeing the graph in a dynamic way.

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