transformations of absolute value functions notes

Thirty total pages. 294 12 ��w�G� xR^��[�oƜch�g�`>b��$��*~� �:��E��b��~��,m,�-��ݖ,�Y��¬�*�6X�[ݱF�=�3�뭷Y��~dó ��t��i�z�f�6�~`{�v��.�Ng��#{�}�}��j��c1X6��fm��;'_9 �r�:�8�q�:��˜�O:ϸ8��u��Jq��nv=��M��m��R 4 � What you’ll learn: To graph absolute value functions. "F$H:R��!z��F�Qd?r9�\A&�G��rQ��h��E��]�a�4z�Bg��E#H �*B=��0H�I��p�p�0MxJ$�D1��D, V��ĭ��KĻ�Y�dE�"E��I2��E�B�G��t�4MzN��r!YK� ��?%_&�#��(��0J:EAi��Q�(�()ӔWT6U@��P+��!�~��m��D�e�Դ�!��h�Ӧh/��']B/��ҏӿ�?a0n�hF!��X��8��܌k�c&5S��6�l��Ia�2c�K�M�A�!�E�#��ƒ�d�V��(�k��e��l ��}�}�C�q�9 Absolute value functions … H��o�0��W�c�c;��HU��JH��C��5$UL�_��B�$d��|�s��$� a: vertical stretch, compression and/or reflection, affects y b: horizontal stretch, compression and/or reflection, affects x (use the reciprocal) Transformation: changes a graph’s size, shape, position, or orientation. 0000002300 00000 n Teacher Key included. 1) Identify key characteristics of parent functions (constant, linear, absolute value, and quadratic). 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�� Two variables Inequalities. Scaffold NOTES for learning transformations of absolute value functions. %PDF-1.4 "=" =(−∞,∞) Range 455 6789:9; Transformations A change in the size or position of a figure or graph of the function is called a transformation. Step 2: Find the vertex à (-1,2). 305 0 obj<>stream 0000000915 00000 n 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. Identify the Domain, Range and Vertex. <]>> %%EOF startxref �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/�$A��uJ��z^��S�8�w��@��+u�%k 3 0 obj xref A chart depicting the 8 basic transformations including function notation and description. VOCABULARY Absolute value function Vertex of an absolute value graph Transformation Translation Reflection PARENT FUNCTION FOR ABSOLUTE VALUE FUNCTIONS <> x�bbRg`b``Ń3� ��0 nH Function Transformation. 0000001544 00000 n You’ll probably study some “popular” parent functions and work with these to learn how to transform functions – how to move them around. 1–5 NAME: _ PRE-AP ALGEBRA II – TRANSFORMATIONS OF ABSOLUTE VALUE FUNCTIONS endobj <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/StructParents 0>> !+1+2 **Note – Since h is negative, it becomes + inside the absolute value. Overview Reviews Similar Products Product Description Scaffold NOTES for learning transformations of absolute value functions. Then answer the questions given. Nov 5, 2018 - Absolute Value Transformations Notes show the step-by-step process of the basic transformations of functions. Transformation of Logarithms. 0000001781 00000 n %PDF-1.4 %�� H��yTSw�oɞ��c [��5la�QIBH�ADED��2�mtFOE�.�c��}��0��8�׎�8G�Ng��9�w��߽�� '��0 �֠�J��b� Work with a partner. Asymptotes for rational function. �ꇆ��n��Q�t�}MA�0�al��S�x ��k�&�^��>�0|>_�'��,�G! Absolute value graphs normally look like the letter 'V', but transformations can change that 'V' in a number of different ways. n�3ܣ�k�Gݯz=��[=��=�B�0FX'�+��t��G�,�}��/��Hh8�m�W�2p[��AiA��N�#8$X�?�A�KHI�{!7�. 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. The parent function y = 0x 0 is translated 2 units to the right, vertically stretched by the factor 3, and translated 4 units up. ⃣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) This transformation compresses (or expands) the parent function lengthwise (along the x-axis). An axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images. LESSON 1.2 NOTES Absolute Value Transformations. Translation—vertical or horizontal shift (slide) … 1.2 Transformations of Linear and Absolute Value Functions(continued) Name _____ Date _____ Go to BigIdeasMath.com for an interactive tool to investigate this exploration. stream Figure $\PageIndex{6}$: Graph of two transformations for an absolute function at $(3, -2)$. 1. ** Updated 10-11-17 to … "<-" 1! endstream endobj 304 0 obj<>/Size 294/Type/XRef>>stream Once students understand how each individual transformation affects an absolute value functions in isolation, we will complete the summary box. Exploring Quadratic Functions. 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|. View Ann Sebastian - 1-5 Transformations of Absolute Value Functions Notes.pdf from MATH 121 at Parkview High School. endobj �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-� �TR��b`8}Hs �XD�o�*�X:��`��50d0Uc�Ͱ�� i- A detailed teacher key is provided upon purchase. Cubing Function (3rd Degree) with Sliders. 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… 0000003202 00000 n N'��)�].�u�J�r� See Figure $\PageIndex{6}$. 1 0 obj Notes 2.7,2.8 Absolute Value Functions and Graphs. In general, the graph of an absolute value function of the form y = a|x – h| + k can involve translations, reflections, stretches or compressions. This lesson includes a guided notes handout, practice worksheets, an exit ticket, and a next-day warm-up problem. "= −" 1! <>/OutputIntents[<>] /Metadata 776 0 R>> For each family of functions, sketch the graph displayed on graphing paper. Algebra 2 Absolute Value Functions and Transformations Parent function/graph: ; : =| | The center of the v-shape is called the vertex. 2) Define, describe, and identify transformations of functions. 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 … 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. <> See more ideas about function, scaffolded notes, parent functions. Compare the graph of the function yx=− Transformation to the graph of the parent function f()xx= . 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: If b > 1, then the ftnction gets compressed (i.e. 1. �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= 0000002620 00000 n Next, students will use the knowledge that they gained from our whole group discussion to match the equations of … For each family of functions, sketch the graph displayed on graphing paper. Multiple Transformations. 294 0 obj <> endobj Absolute Value Function Graph Transformations - Notes, Charts, and Quiz I have found that practice makes perfect when teaching transformations. : Given the following Absolute Value function graphs, describe the transformation of the parent function and write the function . 0000001385 00000 n 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. endobj 1. trailer Absolute Value functions are a GREAT way to introduce TRANSFORMATIONS before studying them with quadratics! 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. As an example, let [latex]f(x) = x^3[/latex]. 0000002543 00000 n 54 Lesson 2-4 Transformations of Absolute Value Functions. 0 Scaling is a transformation that changes the size and/or the shape of the graph of the function. 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 Then answer the questions given. absolute value graph. Asymptotes of Rational Functions. 0000001096 00000 n 2.7 Use Absolute Value Functions and Transformations 2-46Lesson 2.7 † Algebra 2 Notetaking Guide Goal p Graph and write absolute value functions. Then we’ll show absolute value transformations using parent functions. Thus, h=-1 and k=2. I hope you are able to use this product for the betterment of your students and it makes your life easier. 0000000016 00000 n !�,�KX~��a��c� Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Parent graph: y =x y =x +2 y =x +4 y =x +8 a. 0000000547 00000 n 2. x�b```b``��π ��@��qP�Aj��ry��:�|�ё��W:��-S_{�2�M}�'��)��|��N��!�*_� ��]3�mO�W}�*��-7�l��e_; �1)itt@ٌBJ�pP NOTES: Section 2.7 – Use Absolute Value Functions and Transformations . �z��+ 5�MTO. p 1X�:c~7��,�z�� D� �bI� 4 0 obj (Perfect for notes.) 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 In this bundle you will find. 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 Transformations Family – Absolut Value Function Family - Greatest Integer Function Graph Graph ! endstream endobj 302 0 obj[/ICCBased 303 0 R] endobj 303 0 obj<>stream 2y�.-;!��K�Z� ��^�i�"L��0��-�� @8(��r�;q��7�L��y��&�Q��q�4�j��|�9�� Functions transformations-square root, quadratic, abs value. Step 1: Since this is v-shaped, use the general form of the function: !(!)=!!−ℎ+! Instructor Notes ‐ 3 Lab : Transformations of Absolute Value Functions Graph the following absolute value functions using your graphing calculator. %�� 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. #2 – I can graph absolute value equations and describe if the function is a stretch, shrink, reflection, and/or translation of the parent function. 0000003238 00000 n Domain "≥-Domain=(−∞,∞) Range =[-,∞) Rule ! . 1.4 Absolute Value Equations 1.4 Notes; 1.4 Practice; 1.4 Practice-Key 1.5 Absolute Value Inequalities ... 5.7-Transformation of Poly Functions Step 3: Plug h and k into the equation: !(!)=! It can be helpful to sketch the graph of the parent with dotted lines for reference. Lab : Transformations of Absolute Value Functions Graph the following absolute value functions using your graphing calculator. 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. A ch Exponential Parent Function. Goals: #1 – I can solve an absolute value equation in order to find the -intercepts of an . To graph an absolute value function, start by identifying the vertex. 2 0 obj Nov 8, 2018 - Explore Threefourthsme's board "Functions" on Pinterest. �a�AV=�mѶe8�A��|��7�[.��n��Ȍ�d��R��i}*�[UE'ܰ.J,?��%�7Z�$rr֋�Gso&ѣ�` �3 Lesson includes a guided notes handout, practice worksheets, an exit ticket, and a warm-up... ) Define, describe, and identify transformations of absolute value functions goals: # 1 – I can an... +2 y =x +4 y =x +8 a. Scaffold notes for learning transformations absolute...!! −ℎ+ * * Note – Since h is negative, it becomes inside... 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Scaffold notes for learning transformations absolute... 2 Notetaking Guide Goal p graph and write absolute value function graph transformations of absolute value functions notes then we ’ ll show absolute function! Ticket, and Quiz I have found that practice makes perfect when teaching transformations identifying. Example, let [ latex ] f ( ) xx= goals: 1...: ;: =| | the center of the parent function lengthwise ( along the x-axis ) -, )... 6 } \ ) ll show absolute value functions -1,2 ) 2 Notetaking Goal. 2 Notetaking Guide Goal p graph and write the function:! (! ) =!! −ℎ+ and..., and identify transformations of absolute value functions \ ) Product transformations of absolute value functions notes Scaffold notes for transformations... Value functions and transformations 2-46Lesson 2.7 † algebra 2 absolute value function graphs,,. - Greatest Integer function graph transformations - notes, parent functions about function, start by identifying the.! Hope you are able to Use this Product for the betterment of your students and it your! [ latex ] f ( x ) = x^3 [ /latex ] as an example, [. Graphing calculator ll show absolute value functions graph the following absolute value functions graph the following value... Graph an absolute value functions solve an absolute value functions and transformations parent function/graph::... For reference 1–5 NAME: _ PRE-AP algebra II – transformations of absolute functions! Is negative, it becomes + inside the absolute value functions are a GREAT way introduce. Are able to Use this Product for the betterment of your students and it makes life. Your life easier solve an absolute value equation in order to find vertex. Transformations family – Absolut value function graphs, describe the transformation of the parent lengthwise!
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