transformations of absolute value functions notes

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

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