Name LESSON 2-9 Date Class Reteach Absolute-Value Functions The graph of the absolute-value parent function looks like a V. � � � � � To translate f x x to a new vertex h, k , use g x x h k. � �� �� �� �� �� � �� Translate f x x so that the vertex is at 2, 3 . g x x h k Write the transformation. g x x 2 3 Substitute h 2, k 3. g x x 2 3 Simplify. � � � � � � �� �� �� �� Graph to check: � The vertex is 2, 3 . The entire graph of the parent function moves when the vertex moves. � � � ��� � � � �� �� �� �� �� � �� �� � � � � � � � ��� �� �� �� Translate f x x to each new vertex. Then graph the transformation. 1. vertex 1, 2 2. g x x g x � � � � � � � � � � �� �� �� �� �� � �� � � � � � � � � �� �� �� �� �� � �� �� �� �� �� �� �� �� �� Copyright © by Holt, Rinehart and Winston. All rights reserved. a207c02-9_rt.indd 70 vertex 3, 1 70 � � � � � � Holt Algebra 2 12/7/05 6:27:40 PM Name LESSON 2-9 Date Class Reteach Absolute-Value Functions (continued) To vertically stretch or compress f x by a factor of a, use f x r a f x . To horizontally stretch or compress f x by a factor of b, use 1x . f x r f __ b Stretch the graph of f x x 1 vertically by a factor of 2. Y g x a f x g x 2 x 1 Substitute. g x 2 x 2 G X Distribute. F X X Compress the graph of f x x 2 Y 1. horizontally by a factor of __ 2 1x g x f __ b 1 x f 2x g x f ___ 1 __ 2 Substitute. g x 2x 2 2x 2 Simplify. X Perform each transformation. 3. Stretch f x x 1 vertically by a factor of 3. g x 3 x g x a f x ⫺ 1 g x 3 x ⫺ 3 g x 2x ⫹ 1 g x 2x ⫺ 1 4. Stretch f x 4x 1 horizontally by a factor of 2. b 1x f g x f __ 1 __ 2 x g x 4 1 __ 2 x 1 1. 5. Compress f x 4x 2 vertically by a factor of __ 2 1 __ g x a f x Copyright © by Holt, Rinehart and Winston. 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