1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

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Presentation transcript:

1. 3x + 2 = ½ x – 5 2. |3x + 2| > x – 5 < -3x |x + 2| < 15 Algebra II 1

Transformations of parent functions

 Parent function: _______________________ _____________________________________ __  Transformation: _______________________ ________________________________________ ____  Translation: : _________________________ ________________________________________ ____ _____________________________________ __ 3 Algebra II

 Reflection: : ___________________________ ________________________________________ ____  Vertical stretch: ___ _______________________ ________________________________________ ____  Vertical shrink: : _______________________ ________________________________________ ____ 4 Algebra II

 Domain: ____________________________________ __________________________________________ __  Range: _____________________________________ ________________________________________ ____  Domain and Range MUST be written in: ____________________________ 5 Algebra II

 Domain:  Range: 6 Algebra II

 Domain:  Range: 7 Algebra II

 Domain:  Range: 8 Algebra II

9 ConstantLinear f(x) = Domain: Range: f(x) = Domain: Range:

Algebra II 10 Absolute ValueQuadratic f(x) = Domain: Range: f(x) = Domain: Range:

 R x SR y  Reflect over __________ (affect the __-values), _______ (horizontal and vertical), Reflect over __________ (affect the __ -values)  y = -(x)  ______________________________  y = (x – h) _____________________________ (opposite direction)  y = x + k effects y: _____________________ (same direction)  y =(-x)  _____________________________ 11 Algebra II

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Algebra II 13

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Algebra II 17

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Algebra II 21

22 Algebra II 11. Identify the function family of f(x) = 1/3 |-x| + 4 and describe the domain and range. Use a graphing calculator to verify your answers.

23 Algebra II 11 b. Identify the function family of f(x) = -2(x + 3) 2 – 8 and describe the domain and range. Use a graphing calculator to verify your answers.

24 Algebra II

25 Algebra II 13.

26 Algebra II 14.

27 Algebra II 15.

28 Algebra II 16. Graph g(x) = x – 4 and its parent function. Then describe the transformation.

29 Algebra II 17.

30 Algebra II 18. Graph p(x) = -x 2 and its parent function. Then describe the transformation.

31 Algebra II 19. Graph k(x) = -x and its parent function. Then describe the transformation.

32 Algebra II 21. g(x) = x h(x) = (x – 2) m(x) = -|x| 23. g(x) = 2|x| 24. h(x) = ½x g(x) = 3x 26. h(x) = 3/2x c(x) = 0.2 |x – 2| 28. g(x) = - |x + 5| h(x) = -0.25x 2 + 4

33 Algebra II 31. The table shows the height y of a dirt bike x seconds after jumping off a ramp. What type of function can you use to model this data? Estimate the height after 1.75 seconds.

34 Algebra II Use a graphing calculator to graph the function and its parent function. Then describe the transformation. 32. h(x) = -¼x d(x) = 3(x – 1)

35 Algebra II 35.

36 Algebra II Identify the function family to which g belongs. Compare the graph of g to its parent function and describe the transformation. 1. g(x) = -x g(x) = x g(x) = 2 – 0.2x 4. g(x) = 2 I x I g(x) = 2.2(x + 2) 2

37 Algebra II 6.