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

37
1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1

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

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

1. 3x + 2 = ½ x – 5

2. |3x + 2| > 12

3. 4x – 5 < -3x + 2

4. |x + 2| < 15

Algebra II 1

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

Algebra II

Transformations of parent functions

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

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

3Algebra II

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

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)

4Algebra II

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

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

5Algebra II

Page 6: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Domain: [-4,-1]

Range: [-4,∞)

6Algebra II

Page 7: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Domain: [-1,5]

Range: [-4,7]

7Algebra II

Page 8: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Domain: (-∞, ∞)

Range: [0,∞)

8Algebra II

Page 9: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 9

Constant Linear

f(x) = 1

Domain: (-∞,∞)

Range {1}

f(x) = x

Domain: (-∞,∞)

Range: (-∞,∞)

Page 10: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 10

Absolute Value Quadratic

f(x) = |x|

Domain: (-∞,∞)

Range: [0, ∞)

f(x) = x2

Domain: (-∞,∞)

Range: [0, ∞)

Page 11: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

RxSRy

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

11Algebra II

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

Algebra II 12

Linear f(x) = x

Vertical Shrink by a factor of ¼

Reflection over the x-axis

Vertical shift up 8

Page 13: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 13

Constant f(x) = 1

Vertical shift down 4

Page 14: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 14

Absolute Value f(x) = |x|

Horizontal shrink by a Factor of ⅕…….SoIt is also a vertical stretch by a factor of 5

NARROWER

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

Algebra II 15

Quadratic f(x) = x2

Horizontal shift right 1

Vertical shift up 4

Page 16: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 16

Linear f(x) = x

Vertical shift down 7

Page 17: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 17

Constant f(x) = 1

Vertical shift down10

Page 18: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 18

Absolute Value f(x) = |x|

Vertical shiftUp 1

Page 19: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 19

Quadratic f(x) = x2

Reflection overthe x-axis

Page 20: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 20

Quadratic f(x) = x2

Vertical shrink bya factor of ⅛

WIDER

Page 21: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

Algebra II 21

Absolute Value f(x) = |x|

Vertical stretch by a factor of 6 NARROWER

Page 22: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

22Algebra 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.

Page 23: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

23Algebra 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.

Page 24: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

24Algebra II

Page 25: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

25Algebra II

13.

Page 26: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

26Algebra II

14.

Page 27: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

27Algebra II

15.

Page 28: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

28Algebra II

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

Page 29: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

29Algebra II

17.

Page 30: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

30Algebra II

18. Graph p(x) = -x2 and its parent function. Then describe the transformation.

Page 31: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

31Algebra II

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

Page 32: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

32Algebra II

21. g(x) = x + 3

22. h(x) = (x – 2)2

20. m(x) = -|x|

23. g(x) = 2|x|

24. h(x) = ½x2

25. g(x) = 3x

26. h(x) = 3/2x2 + 3

27. c(x) = 0.2 |x – 2|

28. g(x) = - |x + 5| - 3

29. h(x) = -0.25x2 + 4

Page 33: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

33Algebra 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.

Page 34: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

34Algebra II

Use a graphing calculator to graph the function and its parent function. Then describe the transformation.

32. h(x) = -¼x + 5 33. d(x) = 3(x – 1)2 - 1

34.

Page 35: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

35Algebra II

35.

Page 36: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

36Algebra II

Identify the function family to which g belongs. Compare the graph of g to itsparent function and describe the transformation.

1. g(x) = -x + 2

2. g(x) = x2 - 2

3. g(x) = 2 – 0.2x

4. g(x) = 2 I x I - 2

5. g(x) = 2.2(x + 2)2

Page 37: 1. 3x + 2 = ½ x – 5 2. |3x + 2| > 12 3. 4x – 5 < -3x + 2 4. |x + 2| < 15 Algebra II 1.

37Algebra II

6.