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Transformations : Shifting, Reflecting and Stretching Graphs

Transformations : Shifting, Reflecting and Stretching Graphs. GPS Algebra (MM1A1c) Graph transformations of parent functions. GPS Algebra Standards. MM1A1:

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Transformations : Shifting, Reflecting and Stretching Graphs

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  1. Transformations:Shifting, Reflecting and Stretching Graphs GPS Algebra (MM1A1c) Graph transformations of parent functions

  2. GPS Algebra Standards • MM1A1: c. Graphtransformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes

  3. Objectives Students will be able to graph transformations of the six parent functions.

  4. Essential Question How do transformations affect the graphs of functions?

  5. Recall Linear f(x) = x Quadratic f(x) = x2

  6. Recall Cubic f(x) = x3 Absolute Value f(x) = lxl

  7. Recall Square Root f(x) = x3 Rational Function f(x) = 1/x

  8. Transformations y = a(x-h)n + k a represents a vertical stretch h represents a horizontal shift; (left, right) krepresents a vertical shift; (up, down) nrepresents the shape of the function   (ex. n=3 is cubic) http://www.wsd1.org/waec/math/pre-calculus%20advanced/quadratic%20functions/transformations/transintro.htm

  9. Vertical Stretch If a is greaterthan one, it shrinks up and down (skinner) If a is less than one, it stretches left and right (fatter) y = a(x)2 y = x2 = 1(x)2 y = 2(x)2 y = ½(x)2

  10. Vertical Stretch Practice y = x2 y = ¼x2 y = -2x2 y = x2

  11. Horizontal Shift y = (x-h)n*inside the parenthesis y = (x-0)3 = (x)3 y = (x-4)3 y = (x+2)3 moves LEFT moves RIGHT

  12. Vertical Shift y = (x) + k *outside the parenthesis y = (x) + 0 y = (x) + 2y = (x) - 5 moves UP moves DOWN

  13. Vertical Shift Practice y = lxl y = lxl- 4y = lxl- 2 y = lxl+ 5

  14. Examples • y = ½ (x - 4)2 – 2 • y = 2(x - 1)2 + 3 • y = (x - 3)3 – 6 • y = (x + 1)3 + 4 1.) Key points: (2,0), (4, -2), (6,0) 2.) Key points: (0, 5), (1, 3), (2, 5) 3.) Key points: (2, -7), (3, -6), ( 4, -5) 4.) Key points: (-1, 4), (1, ), (2, 13)

  15. Examples f(x) = IxI = Ix+2I = 2Ix+2I -3 f(x) = x2 f(x) = -x2 = -(x2-3) -3 +2 1 1 1 2

  16. Things to Remember • y = a(x)n + k a(vertical stretch) k (vertical shift) • Common Graphs • f(x) = x2, f(x) = x3 • f(x) = lxl, f(x) = f(x) = x

  17. Any Questions Translation Symmetry Vertical Line Test Domain & Range

  18. Next class • More practice with translations of polynomial functions: degree, lead coefficient, and multiplicity of real zeros • Combinations of Functions - Sum - Product - Composition - Difference - Quotient

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