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CA_GPS_16 - y-axis Symmetry with respect to the origin x f...

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 16 2.4 TRANSFORMATIONS OF GRAPHS AND SYMMETRY Class Time: ____________ Date: __________ Useful Techniques: * Vertical shifts: k x f y + = ) ( (shift up by k units) , k x f y ! = ) ( (shift down by k units), 0 > k . * Horizontal shifts: ) ( h x f y + = (shift left by h units) , ) ( h x f y ! = (shift right by h units), 0 > h . * Symmetry with respect to the x -axis: ) ( x f y ! = [Reflection about the x -axis] * Symmetry with respect to the y -axis: ) ( ) ( x f x f = ! , an “Even Function.” [Reflection about the
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Unformatted text preview: y-axis] * Symmetry with respect to the origin: ) ( ) ( x f x f ! = ! , an “Odd Function.” Graph each function using the techniques of shifting, and/or reflecting. Label at least three points on the graph, if any. 1. a) 6 ) ( 2 + = x x f b) 27 ) ( 3 ! = x x f 2. a) 2 ) 4 ( ) ( ! = x x f b) 3 ) 3 ( ) ( + = x x f 3. a) 16 ) ( + = x x f b) 25 ) ( ! = x x f 4. a) 6 ) 4 ( ) ( 2 + ! = x x f b) 3 16 ) ( ! + = x x f 5. a) 2 ) ( + ! = x x g b) 2 ) ( + ! = x x f...
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