2. CHAPTER 4 TRANSFORMATIONS

3.  What you will learn:  Perform translations  Perform compositions  Solve real-life problems involving compositions 4.1 TRANSLATIONS

4.  How can you translate a figure in a coordinate plane? ESSENTIAL QUESTION

5.  Vector  Initial point  Terminal point  Horizontal component  Vertical Component  Component Form  Transformation  Image  Preimage  Translation  Rigid motion  Composition of transformations CORE VOCABULARY

6.  Quantity that has both direction and magnitude or size  Represented by an arrow drawn from one point to another VECTOR

7.  The starting point of a vector INITIAL POINT

8.  Ending point of a vector TERMINAL POINT

9.  The horizontal change from the starting point of a vector to the ending point  Length from left to right HORIZONTAL COMPONENT

10.  The vertical change from the starting point of a vector to the ending point  Length up and down VERTICAL COMPONENT

11.  Combines the horizontal and vertical components  Ordered Pair (h, v) COMPONENT FORM

12.  Function that moves or changes a figure in some way to produce a new figure called an image TRANSFORMATION

13.  A figure that has been transformed  The points on the image are the outputs IMAGE

14.  The original figure before it was transformed  The points on the image are inputs for the transformation PREIMAGE

15.  Moves every point of a figure the same distance in the same direction TRANSLATION

16.  Preserves the length and angle measure  Maps lines to lines, rays to rays, and segments to segments  Also called isometry RIGID MOTION

17.  Two or more transformations are combined to form a single transformation COMPOSITION OF TRANSFORMATIONS

18.  What you will learn:  Perform reflections  Perform glide reflections  Identify lines of symmetry  Solve real life problems involving reflections 4.2 REFLECTIONS

19.  How can you reflect a figure in a coordinate plane? LEAVE 4 LINES ESSENTIAL QUESTION:

20.  Reflection  Line of reflection  Glide reflection  Line symmetry  Line of symmetry CORE VOCABULARY

21.  Transformation that uses a line like a mirror to reflect a figure REFLECTION

22.  The line the figure is reflected over LINE OF REFLECTION

23.  Two step transformation 1. translation (glide) 2. Reflection GLIDE REFLECTION

24.  A figure can be mapped onto itself by a reflection in a line LINE SYMMETRY

25.  Line of reflection LINE OF SYMMETRY

26.  What you will learn:  Perform rotations  Perform compositions with rotations  Identify rotational symmetry 4.3 ROTATIONS

27.  How can you rotate a figure in a coordinate plane? LEAVE 4 LINES ESSENTIAL QUESTION:

28.  Rotation  Center of rotation  Angle of rotation  Rotational symmetry  Center of symmetry CORE VOCABULARY

29.  Transformation  Figure turned about a fixed point ROTATION

30.  the fixed point around which a two- dimensional figure is rotated CENTER OF ROTATION

31.  Rays drawn from the center of rotation to a point and its image from an angle ANGLE OF ROTATION

32.  if an figure looks exactly the same after 180 degrees (a ½ turn or less) ROTATIONAL SYMMETRY

33.  The point the figure is rotated around CENTER OF SYMMETRY

34.  Translation  Reflection  Glide reflection  Rotation CORE CONCEPT: 4 TYPES OF TRANSFORMATIONS

35.  What you will learn:  Graph equations of horizontal and vertical lines  Graph linear equations in standard form using intercepts  Use linear equations in standard form to solve real-life problems 3.4 GRAPHING LINEAR EQUATIONS IN STANDARD FORM

36.  How can you describe the graph of the equation Ax + By = C? LEAVE 4 LINES ESSENTIAL QUESTION:

37.  Ordered Pair  Quadrant PREVIOUS VOCABULARY

38.  Standard form  x-intercept  y-intercept CORE VOCABULARY

39.  Ax + By = C  A, B, and C are numbers  A and B do not equal 0 STANDARD FORM

40.  Where the graph crosses the x-axis  Y=0  (x,0) X-INTERCEPT

41.  Where the graph crosses the y-axis  x=0  (0,y) Y-INTERCEPT

42.  Horizontal Lines  Goes from left to right  Crosses the y-axis  y = a number  No slope CORE CONCEPT

43.  Vertical Lines  Goes up and down  Crosses the x-axis  x = a number  Slope is undefined CORE CONCEPT

44.  What you will learn:  Find the slope of a line  Use the slope intercept form of a linear equation  Use slopes and y-intercepts to solve real-life problems 3.5 GRAPHING LINEAR EQUATIONS IN SLOPE INTERCEPT FORM

45.  How can you describe the graph of the equation y=mx + b? ESSENTIAL QUESTION

46.  Dependent variable  Independent variable PREVIOUS VOCABULARY

47.  Slope  Rise  Run  Slope-intercept form  Constant function CORE VOCABULARY

48.  The ratio of the rise (change in y) to the run (change in x) SLOPE

49.  change in y  Up & down RISE

50.  change in x  Left to right RUN

51. SLOPE INTERCEPT FORM  y = mx + b  b = y-intercept  m = slope

52.  Linear equation  Y=b  Horizontal line CONSTANT FUNCTION

53.  4 types of slope CORE CONCEPT

54.  Graphing Compound inequalities “or”  “or” is the union of the inequality’s solutions  “or” contains all the solutions for both inequalities CORE CONCEPT

55.  What you will learn:  Translate and reflect graphs of linear functions  Stretch and shrink graphs of linear functions  Combine transformations of graphs of linear functions 3.6 TRANSFORMATIONS OF GRAPHS OF LINEAR FUNCTIONS

56.  How does the graph of the linear function f(x) = x compare to the graphs of g(x) = f(x) + c and h(x) = f(cx)? ESSENTIAL QUESTION:

57.  Linear function PREVIOUS VOCABULARY

58.  family of functions  parent function  Transformation  Translation  Reflection  horizontal shrink  horizontal stretch  vertical stretch  vertical shrink CORE VOCABULARY

59.  a group of functions with similar characteristics FAMILY OF FUNCTION

60.  most basic function in a family of functions  For nonconstant linear functions, the parent function is f(x) = x. PARENT FUNCTION

61.  changes the size, shape, position, or orientation of a graph TRANSFORMATION

62.  a transformation that shifts a graph horizontally or vertically but does not change the size, shape, or orientation of the graph. TRANSLATION

63.  a transformation that flips a graph over a line called the line of reflection REFLECTION

64.  When a > 1,  the graph shrinks toward the y-axis  y-intercept stays the same HORIZONTAL SHRINK

65.  When 0 < a < 1  the graph stretches away from the y-axis  y-intercept stays the same HORIZONTAL STRETCH

66.  When a > 1  graph shrinks toward the x- axis  the x-intercept stays the same VERTICAL STRETCH

67.  When 0 < a < 1  graph shrinks toward the x- axis  the x-intercept stays the same VERTICAL SHRINK

68.  What you will learn:  Translate graphs of absolute value functions  Stretch, shrink, and reflect graphs of absolute value functions  Combine transformations of graphs of absolute value functions 3.7 GRAPHING ABSOLUTE VALUE FUNCTIONS

69.  How do the values of a, h, and k affect the graph of the absolute value function g(x) = a ∣ x − h ∣ + k? ESSENTIAL QUESTION:

70.  Domain  Range PREVIOUS VOCABULARY

71.  Absolute value function  Vertex  Vertex form CORE VOCABULARY

72.  Contains an absolute value expression  The parent is f(x)=IxI  It is v-shaped about the y-axis ABSOLUTE VALUE FUNCTION

73.  Point where the graph changes direction  The vertex of the graph of f(x)=IxI is (0,0) VERTEX

74.  g(x)=aIx-hI + k  a≠0  The vertex is (h,k)  Any fuction can be written in this form  Its graph is symmetric about the line x=h VERTEX FORM