Transformations of Parent Functions

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Objective

SWBAT identify the transformations of some Parent Functions developed from the formula f(x)=a(x-h)^2 + k for quadratics.

Big Idea

To develop an understanding for the transformations of parent functions through repeated reasoning (MP8) and the structure (MP7) of the equation.

Warm Up

10 minutes

I expect today's Warm Up to take students about 10 minutes to complete and for me to review with the class.  I ask my students to graph eight different lines to introduce functions that are transformed from their Parent Function.

I will review the graphing of the lines with an interactive tool that can be found at the beginning of the Transformation Power Point that I provide in the resources.  When reviewing the Warm Up, I expect my students to start to recognize the translations and reflections from the Linear Parent Function y=x. I am looking to see if my students can visualize and predict different lines based on the structure of an equation (MP7).  I demonstrate the Warm Up in the video below.

 

Graphing Calculator Activity

30 minutes

After reviewing the Warm Up, I plan to use the Graphing Calculator to introduce the Quadratic Function family to my students.  I do this by demonstrating different Quadratic Functions on the TI-Nspire Cx.  I think seeing different Quadratic Functions on the same graph helps students to use repeated reasoning to better understand the relationship between an equation and its graph (MP8).

Teacher's Note: For my students, I think that the Quadratic Function is the easiest function to use when I want them to see the effect of transformations.  I demonstrate this activity in this video Quadratic Function Transformations.  I do not refer to the formula at first, I use the graphing calculator as a visual for students to recognize how the structure of the equation is related to the graph.

My students have calculators in their hands throughout this activity. I want them to be able to enter the different Quadratic Functions along with me.  I refer back to the Transformation Power Point pages that I have copied for students to sketch a few different graphs to keep as notes.  I refer to the general equation at this time.  I ask students to explain by looking at the equation why the horizontal shift (h) is opposite of the number inside the function.  Also that the vertical shift is the identical number that is represented in the function.  I want my students to recognize that the formula minus h refers to the opposite number and that plus k refers to the identical number.

I am careful to write the words shift right, shift left, shift up, shift down, and reflect over. I want to make sure that students use common terms in their notes.

Once students seem comfortable with the Quadratics, I will use the calculator to graph a few members of the Exponential Function family. Using the PowerPoint, I help my students recognize the similarities in the structure of the general equations. My students are usually quick to see that minus h and plus k will result in the same translations for exponential functions as for Quadratic Functions.  

Finally, I introduce the Square Root Function family, and again refer back to the Power Point Page for students to  sketch in the notes.  I have provided a List of Functions that I model during the Calculator Activities. 

Exit Slip

5 minutes

After working with the students on recognizing the transformations of functions from a Parent Function, I provide the students an Exit Slip.  I use the Exit Slip as a quick formative assessment to check for student understanding of the transformations of different functions.  

I expect that today my students will be able to predict the transformations of the functions given from the Parent Function 3^x by the structure of the equation (MP7).  After the students predict the transformation of each function, I instruct them to check it with a graphing calculator. Students then provide feedback to me on the Exit Slip about which functions they had difficulty predicting. Students had the most difficulty predicting what would happen when two to the x power was reflected across the x axis with the equation negative two to the x power.