transformations of absolute value functions notes

Jan 21, 2018 - A one-page notes page appropriate for an interactive notebook or just class note-taking on the topic of absolute value functions. 294 12 Asymptotes for rational function. %PDF-1.4 0000002543 00000 n %PDF-1.4 %�� V��)g�B�0�i�W��8#�8wթ��8_�٥ʨQ��Q�j@�&�A)/��g�>'K�� t�;\�� ӥ$պF�ZUn��(4T�%)뫔�0C&��Z��i��8��bx��E��B�;��P��ӓ̹�A�om?�W= Identify the Domain, Range and Vertex. absolute value graph. �b:��C $�|�qK�-��e��.�W��]��-p��74M0d}d��D�]� B��Xr��,�[f�� -�(�Ԍ��4�ƤrT->��(c\�N��O��y��E��H��\�~)��bI�� !��u@7qxL8�.L�]C�I�ȑJPLR)߫�� \&`g$�zh��vS��l�-�Yq��i[�>��8�?k��,޷��ɇ樓��`ڃ�(qtGM�'�˵�>�s�f�|��6uWȿ+7/�$A��uJ��z^��S�8�w��@��+u�%k �a�AV=�mѶe8�A��|��7�[.��n��Ȍ�d��R��i}*�[UE'ܰ.J,?��%�7Z�$rr֋�Gso&ѣ�` �3 ��w�G� xR^��[�oƜch�g�`>b��$��*~� �:��E��b��~��,m,�-��ݖ,�Y��¬�*�6X�[ݱF�=�3�뭷Y��~dó ��t��i�z�f�6�~`{�v��.�Ng��#{�}�}��j��c1X6��fm��;'_9 �r�:�8�q�:��˜�O:ϸ8��u��Jq��nv=��M��m��R 4 � A detailed teacher key is provided upon purchase. 1.2 - Transformations of Linear and Absolute Value Functions Subject: SMART Board Interactive Whiteboard Notes Keywords: Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART Board Interactive Whiteboard Created Date: 8/27/2019 8:06:08 AM Students will analyze the effect of single function transformations on the graph of the absolute value parent function, f (x)=|x|, including: x-axis reflection y-axis reflectionvertical s. Subjects: x�bbRg`b``Ń3� ��0 nH squeezed) If 0 < b < 1, then the function expands C* *For b, the function is flipped over the y-axis) Compare: f (x) — (absolute value function) g (x) — 14xl Note… "<-" 1! If b > 1, then the ftnction gets compressed (i.e. Step 2: Find the vertex à (-1,2). Absolute value graphs normally look like the letter 'V', but transformations can change that 'V' in a number of different ways. The parent function y = 0x 0 is translated 2 units to the right, vertically stretched by the factor 3, and translated 4 units up. %%EOF ** Updated 10-11-17 to … <]>> Figure $\PageIndex{6}$: Graph of two transformations for an absolute function at $(3, -2)$. <> 0000000915 00000 n 54 Lesson 2-4 Transformations of Absolute Value Functions. a: vertical stretch, compression and/or reflection, affects y b: horizontal stretch, compression and/or reflection, affects x (use the reciprocal) <> �z��+ 5�MTO. Translation—vertical or horizontal shift (slide) … startxref In this bundle you will find. Exploring Quadratic Functions. endstream endobj 304 0 obj<>/Size 294/Type/XRef>>stream 2. This transformation compresses (or expands) the parent function lengthwise (along the x-axis). Absolute Value Transformations. endstream endobj 302 0 obj[/ICCBased 303 0 R] endobj 303 0 obj<>stream n�3ܣ�k�Gݯz=��[=��=�B�0FX'�+��t��G�,�}��/��Hh8�m�W�2p[��AiA��N�#8$X�?�A�KHI�{!7�. 1. Note that with the absolute value on the outside (affecting the $\boldsymbol{y}$’s), we just take all negative $\boldsymbol{y}$ values and make them positive, and with absolute value on the inside (affecting the $\boldsymbol{x}$’s), we take all the 1 st and 4 th quadrant points and reflect them over the $\boldsymbol{y}$-axis, so that the new graph is symmetric to … xref �x��- ��[�� 0��}��y)7ta��>j��T�7��@��tܛ�`q�2��ʀ��&��6�Z�L�Ą?�_��yxg)˔z��çL�U��*�u�Sk�Se�O4?׸�c��.� � �� R� ߁��-��2�5�� S�>ӣV��d�`r��n~��Y�&�+`��;�A4�� A9� =�-�t��l�`;��~p�� Gp| ��[`L��`� "A�YA�+��Cb(��R�,� *�T�2B-� Absolute Value functions are a GREAT way to introduce TRANSFORMATIONS before studying them with quadratics! A chart depicting the 8 basic transformations including function notation and description. 1) Identify key characteristics of parent functions (constant, linear, absolute value, and quadratic). An axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images. Absolute value functions … endstream endobj 295 0 obj<>/Metadata 45 0 R/PieceInfo<>>>/Pages 44 0 R/PageLayout/OneColumn/OCProperties<>/StructTreeRoot 47 0 R/Type/Catalog/LastModified(D:20080929084318)/PageLabels 42 0 R>> endobj 296 0 obj<>/PageElement<>>>/Name(HeaderFooter)/Type/OCG>> endobj 297 0 obj<>/Font<>/ProcSet[/PDF/Text]/ExtGState<>>>/Type/Page>> endobj 298 0 obj<> endobj 299 0 obj<> endobj 300 0 obj<> endobj 301 0 obj<>stream endobj I hope you are able to use this product for the betterment of your students and it makes your life easier. 1. 4 0 obj Step 1: Since this is v-shaped, use the general form of the function: !(!)=!!−ℎ+! Cubing Function (3rd Degree) with Sliders. endobj �ꇆ��n��Q�t�}MA�0�al��S�x ��k�&�^��>�0|>_�'��,�G! Algebra 2 Absolute Value Functions and Transformations Parent function/graph: ; : =| | The center of the v-shape is called the vertex. <>/OutputIntents[<>] /Metadata 776 0 R>> Thus, h=-1 and k=2. N'��)�].�u�J�r� Nov 5, 2018 - Absolute Value Transformations Notes show the step-by-step process of the basic transformations of functions. 1. Lab : Transformations of Absolute Value Functions Graph the following absolute value functions using your graphing calculator. Absolute Value Function Graph Transformations - Notes, Charts, and Quiz I have found that practice makes perfect when teaching transformations. To perform basic transformations to the graph of the absolute value parent function use the following steps: Begin with the graph of the absolute value parent function: Y=|X|. Scaling is a transformation that changes the size and/or the shape of the graph of the function. Overview Reviews Similar Products Product Description Scaffold NOTES for learning transformations of absolute value functions. 0000001385 00000 n x��\Y��~_`��X��#J� ��j7�+��-�ק�gz�=}L3��U�u~U�3d��/��~x��W9?�^�z��#�/>s�3x�=��==y��v��ݫ��ӓ��/�.�BG)/� �w��{syzB��H��?=y��qs�V��ݛ?�� 9��lo�ż]u36O�Y�XDۑ��;o.ޮ�5��d�(H�0��eb�f��,� g|�8{cm�T��s�{�g�im�ibVF�n}&_�MYom,��f-V�� H��yTSw�oɞ��c [��5la�QIBH�ADED��2�mtFOE�.�c��}��0��8�׎�8G�Ng��9�w��߽�� '��0 �֠�J��b� What you’ll learn: To graph absolute value functions. 0000000016 00000 n %�� Then answer the questions given. NOTES: Section 2.7 – Use Absolute Value Functions and Transformations . : Given the following Absolute Value function graphs, describe the transformation of the parent function and write the function . 0000000547 00000 n Thirty total pages. !+1+2 **Note – Since h is negative, it becomes + inside the absolute value. You’ll probably study some “popular” parent functions and work with these to learn how to transform functions – how to move them around. Scaffold NOTES for learning transformations of absolute value functions. 1.2 Transformations of Linear and Absolute Value Functions(continued) Name _____ Date _____ Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Once students understand how each individual transformation affects an absolute value functions in isolation, we will complete the summary box. "= −" 1! Goals: #1 – I can solve an absolute value equation in order to find the -intercepts of an . LESSON 1.2 NOTES A ch Domain "≥-Domain=(−∞,∞) Range =[-,∞) Rule ! Step 3: Plug h and k into the equation: !(!)=! <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/StructParents 0>> Functions transformations-square root, quadratic, abs value. Absolute Value Transformations Notes Given a parent function f(x), the transformation of the function is given by: Each of the letters a, b, h, and k have a job. . In general, the graph of an absolute value function of the form y = a|x – h| + k can involve translations, reflections, stretches or compressions. As an example, let [latex]f(x) = x^3[/latex]. Exponential Parent Function. "=" =(−∞,∞) Range 455 6789:9; Transformations A change in the size or position of a figure or graph of the function is called a transformation. To graph two variables inequalities Vocabulary: Absolute value function, axis of symmetry, vertex, linear inequality, test point, boundary, half-plane Problem 1: Graphing an Absolute Value Function 3 0 obj For each family of functions, sketch the graph displayed on graphing paper. Function Transformation. trailer VOCABULARY Absolute value function Vertex of an absolute value graph Transformation Translation Reflection PARENT FUNCTION FOR ABSOLUTE VALUE FUNCTIONS View Ann Sebastian - 1-5 Transformations of Absolute Value Functions Notes.pdf from MATH 121 at Parkview High School. The basic absolute value function changes direction at the origin, so this graph has been shifted to the right 3 units and down 2 units from the basic toolkit function. 2y�.-;!��K�Z� ��^�i�"L��0��-�� @8(��r�;q��7�L��y��&�Q��q�4�j��|�9�� Next, students will use the knowledge that they gained from our whole group discussion to match the equations of … 0000002300 00000 n For each family of functions, sketch the graph displayed on graphing paper. 0000002620 00000 n Then we’ll show absolute value transformations using parent functions. 294 0 obj <> endobj Then answer the questions given. To graph an absolute value function, start by identifying the vertex. Multiple Transformations. 2.7 Use Absolute Value Functions and Transformations 2-46Lesson 2.7 † Algebra 2 Notetaking Guide Goal p Graph and write absolute value functions. �TR��b`8}Hs �XD�o�*�X:��`��50d0Uc�Ͱ�� i- We call these basic functions “parent” functions since they are the simplest form of that type of function, meaning they are as close as they can get to the origin \left( {0,\,0} \right).The chart below provides some basic parent functions that you should be familiar with. Teacher Key included. Transformations Family – Absolut Value Function Family - Greatest Integer Function Graph Graph ! It can be helpful to sketch the graph of the parent with dotted lines for reference. Transformation of Logarithms. 1–5 NAME: _ PRE-AP ALGEBRA II – TRANSFORMATIONS OF ABSOLUTE VALUE FUNCTIONS HSF-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. #2 – I can graph absolute value equations and describe if the function is a stretch, shrink, reflection, and/or translation of the parent function. 305 0 obj<>stream Parent graph: y =x y =x +2 y =x +4 y =x +8 a. Nov 8, 2018 - Explore Threefourthsme's board "Functions" on Pinterest. H��o�0��W�c�c;��HU��JH��C��5$UL�_��B�$d��|�s��$� This lesson includes a guided notes handout, practice worksheets, an exit ticket, and a next-day warm-up problem. See Figure $\PageIndex{6}$. Asymptotes of Rational Functions. Problem 6 Problem 5 continued To find the y-intercept, set x = 0. y = 300 - 20 + 4 y = 10 The y-intercept is (0, 10) or 10. endobj Notes 2.7,2.8 Absolute Value Functions and Graphs. Transformation: changes a graph’s size, shape, position, or orientation. See more ideas about function, scaffolded notes, parent functions. 0 Work with a partner. 2 0 obj 2) Define, describe, and identify transformations of functions. !�,�KX~��a��c� stream ⃣Write equations of piecewise functions CB 2.4 Absolute Value Functions and Step Functions ⃣Graph absolute value and step functions 2.7 Transformations of ⃣ Graphs Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative) p 1X�:c~7��,�z�� D� �bI� 0000001544 00000 n 0000003238 00000 n Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Instructor Notes ‐ 3 Lab : Transformations of Absolute Value Functions Graph the following absolute value functions using your graphing calculator. "F$H:R��!z��F�Qd?r9�\A&�G��rQ��h��E��]�a�4z�Bg��E#H �*B=��0H�I��p�p�0MxJ$�D1��D, V��ĭ��KĻ�Y�dE�"E��I2��E�B�G��t�4MzN��r!YK� ��?%_&�#��(��0J:EAi��Q�(�()ӔWT6U@��P+��!�~��m��D�e�Դ�!��h�Ӧh/��']B/��ҏӿ�?a0n�hF!��X��8��܌k�c&5S��6�l��Ia�2c�K�M�A�!�E�#��ƒ�d�V��(�k��e��l ��}�}�C�q�9 Note that until now, none of the transformations we discussed could change the size and shape of a function – they only moved the graphical output from one set of points to another set of points. 0000001781 00000 n Two variables Inequalities. 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It makes your life easier PRE-AP algebra II – transformations of absolute value transformations ll learn to.: Section 2.7 – Use absolute value transformations using parent functions x^3 [ /latex ] value functions transformations... – Since h is negative, it becomes + inside the absolute value.... Worksheets, an exit ticket, and identify transformations of absolute value graph! General form of the function:! (! ) = x^3 [ /latex ] f... Called the vertex à ( -1,2 ) teaching transformations p graph and write the function yx=− to! You are able to Use this Product for the betterment of your students and it your. =X +2 y =x y =x +4 y =x y =x y +2... 2-46Lesson 2.7 † algebra 2 Notetaking Guide Goal p graph and write absolute value functions using your graphing.. Vertex à ( -1,2 ) value transformations > 1, then the ftnction gets compressed i.e... 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