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

2. Transformations of parent functions

3.  Parent function:  the most basic graph in a family of graphs  Transformation  A change in size, shape, position, or orientation of a graph  Translation  A transformation that shifts a graph horizontally or vertically but does not change size or shape 3 Algebra II

4.  Reflection  A transformation that flips a graph over a line of reflection  Vertical stretch  A transformation that causes the graph of a function to stretch away from the x axis. (multiplied by a factor >1)  Vertical shrink  A transformation that causes the graph of a function to shrink toward the x-axis (multiplied by a factor 0<a<1) 4 Algebra II

5.  Domain:  The x values of a graph, the distance from left to right  Range :  the y values of a graph, the distance from bottom to top ** Domain and Range must be written in: INTERVAL NOTATION 5 Algebra II

6.  Domain:  [-4,-1]  Range:  [-4,∞) 6 Algebra II

7.  Domain:  [-1,5]  Range:  [-4,7] 7 Algebra II

8.  Domain:  (-∞, ∞)  Range:  [0,∞) 8 Algebra II

9. 9 ConstantLinear f(x) = 1 Domain: (-∞,∞) Range {1} f(x) = x Domain: (-∞,∞) Range: (-∞,∞)

10. Algebra II 10 Absolute ValueQuadratic f(x) = |x| Domain: (-∞,∞) Range: [0, ∞) f(x) = x 2 Domain: (-∞,∞) Range: [0, ∞)

11.  R x SR y  Reflect over x-axis (affect the y-values), Shift (horizontal and vertical), Reflect over y-axis (affect the x-values)  y = -(x)  effects y so flips over x axis  y = (x – h) effects x: shift left/right (opposite direction)  y = x + k effects y: shift up/down (same direction)  y =(-x)  effects x so reflect over y 11 Algebra II

12. 12 Linear f(x) = x Vertical Shrink by a factor of ¼ Reflection over the x-axis Vertical shift up 8

13. Algebra II 13 Constant f(x) = 1 Vertical shift down 4

14. Algebra II 14 Absolute Value f(x) = |x| Horizontal shrink by a Factor of ⅕ …….So It is also a vertical stretch by a factor of 5 NARROWER

15. Algebra II 15 Quadratic f(x) = x 2 Horizontal shift right 1 Vertical shift up 4

16. Algebra II 16 Linear f(x) = x Vertical shift down 7

17. Algebra II 17 Constant f(x) = 1 Vertical shift down 10

18. Algebra II 18 Absolute Value f(x) = |x| Vertical shift Up 1

19. Algebra II 19 Quadratic f(x) = x 2 Reflection over the x-axis

20. Algebra II 20 Quadratic f(x) = x 2 Vertical shrink by a factor of ⅛ WIDER

21. Algebra II 21 Absolute Value f(x) = |x| Vertical stretch by a factor of 6 NARROWER

22. 22 Algebra II 11. Identify the function family of f(x) = ⅓|-x| + 4 and describe the domain and range. Use a graphing calculator to verify your answers.

23. 23 Algebra II 11b. 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. 24 Algebra II

25. 25 Algebra II 13.

26. 26 Algebra II 14.

27. 27 Algebra II 15.

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

29. 29 Algebra II 17.

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

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

32. 32 Algebra II 21. g(x) = x + 3 22. h(x) = (x – 2) 2 20. m(x) = -|x| 23. g(x) = 2|x| 24. h(x) = ½x 2 25. g(x) = 3x 26. h(x) = 3/2x 2 + 3 27. c(x) = 0.2 |x – 2| 28. g(x) = - |x + 5| - 3 29. h(x) = -0.25x 2 + 4

33. 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. 34 Algebra II Use a graphing calculator to graph the function and its parent function. Then describe the transformation. 32. h(x) = -¼x + 533. d(x) = 3(x – 1) 2 - 1 34.

35. 35 Algebra II 35.

36. 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 + 2 2. g(x) = x 2 - 2 3. g(x) = 2 – 0.2x 4. g(x) = 2 I x I - 2 5. g(x) = 2.2(x + 2) 2

37. 37 Algebra II 6.