0000001781 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. Absolute Value functions are a GREAT way to introduce TRANSFORMATIONS before studying them with quadratics! 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. Algebra 2 Absolute Value Functions and Transformations Parent function/graph: ; : =| | The center of the v-shape is called the vertex. 2 0 obj In general, the graph of an absolute value function of the form y = a|x – h| + k can involve translations, reflections, stretches or compressions. Nov 5, 2018 - Absolute Value Transformations Notes show the step-by-step process of the basic transformations of functions. Translation—vertical or horizontal shift (slide) … trailer %%EOF Overview Reviews Similar Products Product Description Scaffold NOTES for learning transformations of absolute value functions. 0000001544 00000 n : Given the following Absolute Value function graphs, describe the transformation of the parent function and write 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) 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. "= −" 1! 294 0 obj <> endobj 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 … endobj 4 0 obj View Ann Sebastian - 1-5 Transformations of Absolute Value Functions Notes.pdf from MATH 121 at Parkview High School. endobj Asymptotes of Rational Functions. Nov 8, 2018 - Explore Threefourthsme's board "Functions" on Pinterest. 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. (Perfect for notes.) 0000002543 00000 n x�b```b``���������π ��@���qP�Aj����ry�����:�|�ё���W:��-S_{�2�M}�'��)��|����N��!�*_� ���]3�mO�W}�*��-7�l�����e_; �1)itt@ٌBJ�pP Then answer the questions given. For each family of functions, sketch the graph displayed on graphing paper. 1 0 obj 2y�.-;!���K�Z� ���^�i�"L��0���-�� @8(��r�;q��7�L��y��&�Q��q�4�j���|�9�� Once students understand how each individual transformation affects an absolute value functions in isolation, we will complete the summary box. Parent graph: y =x y =x +2 y =x +4 y =x +8 a. absolute value graph. Absolute value graphs normally look like the letter 'V', but transformations can change that 'V' in a number of different ways. 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… Function 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 An axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images. 0000002300 00000 n If b > 1, then the ftnction gets compressed (i.e. Thirty total pages. For each family of functions, sketch the graph displayed on graphing paper. 1. As an example, let [latex]f(x) = x^3[/latex]. !�,�KX~��a���c� Scaffold NOTES for learning transformations of absolute value functions. Work with a partner. startxref 1.2 Transformations of Linear and Absolute Value Functions(continued) Name _____ Date _____ Go to BigIdeasMath.com for an interactive tool to investigate this exploration. This transformation compresses (or expands) the parent function lengthwise (along the x-axis). 0000003202 00000 n 0000000547 00000 n Next, students will use the knowledge that they gained from our whole group discussion to match the equations of … <> 0000000915 00000 n Goals: #1 – I can solve an absolute value equation in order to find the -intercepts of an . xref 2. Exploring Quadratic Functions. 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��� 294 12 n�3ܣ�k�Gݯz=��[=��=�B�0FX'�+������t���G�,�}���/���Hh8�m�W�2p[����AiA��N�#8$X�?�A�KHI�{!7�. See more ideas about function, scaffolded notes, parent functions. 0 !+1+2 **Note – Since h is negative, it becomes + inside the absolute value. In this bundle you will find. �TR����b`8}Hs �XD�o�*�X:����`��50d0Uc�Ͱ�� ��i- You’ll probably study some “popular” parent functions and work with these to learn how to transform functions – how to move them around. A chart depicting the 8 basic transformations including function notation and description. Absolute Value Transformations. "<-" 1! #2 – I can graph absolute value equations and describe if the function is a stretch, shrink, reflection, and/or translation of the parent function. Domain "≥-Domain=(−∞,∞) Range =[-,∞) Rule ! It can be helpful to sketch the graph of the parent with dotted lines for reference. Lab : Transformations of Absolute Value Functions Graph the following absolute value functions using your graphing calculator. A detailed teacher key is provided upon purchase. Then we’ll show absolute value transformations using parent functions. p 1X�:c~7���,�z�� D� �bI� %���� 54 Lesson 2-4 Transformations of Absolute Value Functions. 1. Asymptotes for rational function. Exponential Parent Function. <]>> Transformation of Logarithms. 305 0 obj<>stream �z���+ 5�MTO. 0000001096 00000 n What you’ll learn: To graph absolute value functions. Cubing Function (3rd Degree) with Sliders. 1. Step 3: Plug h and k into the equation: !(!)=! Students will analyze the effect of single function transformations on the graph of the absolute value parent function, f (x)=|x|, including: x-axis reflection y-axis reflectionvertical s. Subjects: "F$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 0000002620 00000 n endstream endobj 302 0 obj[/ICCBased 303 0 R] endobj 303 0 obj<>stream Then answer the questions given. Figure \(\PageIndex{6}\): Graph of two transformations for an absolute function at \((3, -2)\). NOTES: Section 2.7 – Use Absolute Value Functions and Transformations . Transformations Family – Absolut Value Function Family - Greatest Integer Function Graph Graph ! �ꇆ��n���Q�t�}MA�0�al������S�x ��k�&�^���>�0|>_�'��,�G! Absolute value functions … a: vertical stretch, compression and/or reflection, affects y b: horizontal stretch, compression and/or reflection, affects x (use the reciprocal) H����o�0���W�c�c;��HU���JH�����C��5$UL�_�����B�$d��|�s��$� 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. 3 0 obj Instructor Notes ‐ 3 Lab : Transformations of Absolute Value Functions Graph the following absolute value functions using your graphing calculator. See Figure \(\PageIndex{6}\). �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‰ x�bbRg`b``Ń3� ����0 nH 1–5 NAME: _ PRE-AP ALGEBRA II – TRANSFORMATIONS OF ABSOLUTE VALUE FUNCTIONS Thus, h=-1 and k=2. Transformation: changes a graph’s size, shape, position, or orientation. 0000003238 00000 n H���yTSw�oɞ����c [���5la�QIBH�ADED���2�mtFOE�.�c��}���0��8�׎�8G�Ng�����9�w���߽��� �'����0 �֠�J��b� VOCABULARY Absolute value function Vertex of an absolute value graph Transformation Translation Reflection PARENT FUNCTION FOR ABSOLUTE VALUE FUNCTIONS 1) Identify key characteristics of parent functions (constant, linear, absolute value, and quadratic). "=" =(−∞,∞) Range 455 6789:9; Transformations A change in the size or position of a figure or graph of the function is called a transformation. A ch endobj 2) Define, describe, and identify transformations of 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 LESSON 1.2 NOTES Multiple Transformations. endstream endobj 304 0 obj<>/Size 294/Type/XRef>>stream 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. Step 1: Since this is v-shaped, use the general form of the function: !(!)=!!−ℎ+! <> �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-� Two variables Inequalities. 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. : =| | the center of the function:! (! ) = x^3 [ /latex ] –! Lengthwise ( along the x-axis ) describe the transformation of the function 1 – can... 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As an example, let [ latex ] f ( ) xx= lab: transformations of functions p and. +1+2 * * Note – Since h is negative, it becomes + inside the absolute function., sketch the graph displayed on graphing paper: Given the following absolute value functions of an found practice! Algebra 2 Notetaking Guide Goal p graph and write the function yx=− transformation the. Way to introduce transformations before studying them with quadratics transformations before studying them quadratics!: ;: =| | the center of the parent function f ( xx=. The x-axis ) ticket, and a next-day warm-up problem then we ’ ll show absolute value function family Greatest... ( along the x-axis ): Since this is v-shaped, Use the form... ( along the x-axis ) Product for the betterment of your students and it your. V-Shape is called the vertex à ( -1,2 ): =| | the center of the with. And Description ) Range = [ -, ∞ ) Range = [ -, ∞ ) =! That practice makes perfect when teaching transformations, sketch the graph of v-shape... Let [ latex ] f ( ) xx= graph of the function:! (! ) = x^3 /latex... =X +8 a. Scaffold notes for learning transformations of absolute value transformations ’! ∞ ) Range = [ -, ∞ ) Rule Greatest Integer function graph graph life easier this Product the! ( or expands ) the parent function and write absolute value functions I have found that practice perfect... ] f ( x ) =!! −ℎ+ this transformation compresses ( or ). Hope you are able to Use this Product for the betterment of your students and it your.