Transformations of Rational Functions

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Objective

Students will be able to graph rational functions using transformations.

Big Idea

Our study of transformations on functions is continued in this rational function lesson

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogenous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Transformations of Rational Functions which asks students to describe the transformations on an absolute value function.    

I also use this time to correct and record the previous day's Homework.  

Building Transformations on Rational Functions

38 minutes

We begin by looking at the two basic rational parent functions and their features.  This is the basis for the rest of the lesson.  The students create a table, graph each  function, and determine the domain and range.  We also look at the equations of each asymptotes and discuss why the function is undefined at these points (Math Practice 2). 

Next, we investigate vertical reflections, and horizontal and vertical translations individually.   Rather than identify the domain, range and asymptotes of each function we graph, I have the students identify any differences between its properties and the parent function.  

The students then graph several functions with multiple transformations.  Finally, the students  find the function given information or a graph which deepens their understanding of transformations on rational functions.  

Detailed presentation notes are located in the PowerPoint.

Exit Ticket

2 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

Today's Exit Ticket asks students to graph rational functions using transformations.

Homework

This Assignment begins with a small number of rational functions to graph.  While brief, these problems reinforce the graphing skill.  The final three problems look at these transformations in different ways to ensure that student understand their structure (Math Practice 7).

This assignment was created with Kuta Software, an amazing resource for secondary mathematics teachers.