Match. Let’s take the same function we used above (in red), and graph $$f\left(\left|x\right|\right)$$ (in blue): As explained, we ignore what was on the left side, and replace it with a reflected copy of the right. Describe the transformations of the absolute value equation. That is, all the other “inside” transformations did something to x that could be reversed, so that any input given to the function only occurred for one value of x (shifted or stretched or reflected); but the absolute value means that we will get the same point from two different inputs, on … <>>> Your email address will not be published. There are three types of transformations: translations, reflections, and dilations. Algebraically, for whatever the input value is, the output is … To graph an absolute value function, start by identifying the vertex. �;%v�����;��!k���hvff0H�h���}k] �?n�!%ֵ܀n��g��K���G=2���:����LA��6fh���+���r���WÐf��=�(&@%���]�a��~���qJUV��5̈�m��N�.����V���e�a����Ѐ������*txhÁY�!����uF�4�zD��+n������sp3��qDF��M��vԃ3X����P�>�؍YB|L��~1��W]�#���_�Ï�n�5}Lw\���0e�}�N%z;U_�+9=��(p(x�x��k�|��y��4>5�FY��g}Z�B� �/�2ض.�ۆw Z�������!R��� f (x) = {x if x > 0 0 if x = 0 − x if x < 0. Absolute value graphs, represented by the y=|x| equation, and the transformations that modify this equation, represented by the y=|x-h|+k equation, are important concepts in algebra. Test. example. Why it moves 3 to the right is because you can move graphs around. Absolute Value Functions and Transformations INB Pages The absolute value function is usually the first parent function that is taught in Algebra 2. I left the specific graph for a later question if she needed more help, and focused on the bigger issues that would allow her to work on the problem herself. (In fact, what we are doing here is taking the square root of the blue graph, to make the red one!). Absolute Value Transformations can be tricky, since we have two different types of problems: Transformations of Absolute Value Functions; Performing Absolute Value Transformations on other functions; Transformations of the Absolute Value Parent Function. Having looked at all the usual transformations of a function and its graph, there are two more situations I want to look at. Spell. Untitled Document. V���o����|�9_�(J�'h�t''�Y� The first of these are the horizontal and vertical transformations introduced by absolute values (with a bonus thrown in: square roots); then next time we’ll conclude this series with a look at the special needs of trigonometric functions. Let’s first work with transformations on the absolute value parent function. We’ll be seeing this idea next time.). Plan your 60-minute lesson in Math or Algebra with helpful tips from Amelia Jamison Absolute Value Transformations. When you graph the absolute value function it makes a sudden sharp turn when you get to 0, which in other words is saying when you SWITCH SIGNS fro the negative numbers to non negative, the graph turns. Created by. As a group, define each of these without your book. Absolute Value Transformations Game Show Activity. Now we come to the really tricky case (but it’s really easy): $$f\left(\left|x\right|\right)$$, from 2013: The first two cases are familiar to us now; I made a rough sketch of the graph Pavan described, and did a shift for the first: (You may notice my shortcut: I really used the same graph and just moved the axes. �Ԣ��Fp�m��B��uID ˣ��82h��U�|0��|~�d�uAeUʺ Some of the worksheets for this concept are Name date, Name period transformations work use a calculator, 1 exploration transformations of the absolute value function, Topic 2 absolute value review for semester exam, Transformations of linear and absolute value functions, … The absolute value parent function, written as f (x) = | x |, is defined as . 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