CA_GPS_17 - COLLEGE ALGEBRA NAME:...

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Unformatted text preview: COLLEGE ALGEBRA NAME: ________________________________ GPS # 17 Class Time: ____________ Date: __________ 2.4 TRANSFORMATIONS OF GRAPHS AND SYMMETRY II Useful Techniques: * Vertical shifts: y = f ( x) + k (shift up by k units) , y = f ( x) ! k (shift down by k units), k > 0 . * Horizontal shifts: y = f ( x + h) (shift left by h units) , y = f ( x ! h) (shift right by h units), h > 0 . * Reflection about the x-axis: y = ! f ( x) . * Reflection about the y-axis: y = f (! x) . * Compressing or stretching: For y = af ( x), a > 0 (stretch vertically if a > 1 and compress vertically if 0 < a < 1 ). For y = f (ax), a > 0 (compress horizontally if a > 1 and stretch horizontally if 0 < a < 1 ). Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Label at least three points on the graph. 1. a) g ( x) = ! x 2 + 4 b) g ( x) = ! x 3 ! 8 2. a) f ( x) = ! x + 8 b) f ( x) = x + 4 + 8 3. a) f ( x) = !2 x 2 + 8 b) 1 f ( x) = ! x 2 + 4 4 4. a) f ( x) = !2 x b) f ( x) = x + 3 ! 5 5. a) g ( x) = ! b) g ( x) = ! Rev. S08 1 +2 x 1 +4 ( x ! 2) http://faculty.valenciacc.edu/ashaw/ ...
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