CHAPTER 4 TRANSFORMATIONS

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

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

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

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

 The starting point of a vector INITIAL POINT

 Ending point of a vector TERMINAL POINT

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

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

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

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

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

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

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

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

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

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

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

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

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

 The line the figure is reflected over LINE OF REFLECTION

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

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

 Line of reflection LINE OF SYMMETRY

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

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

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

 Transformation  Figure turned about a fixed point ROTATION

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

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

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

 The point the figure is rotated around CENTER OF SYMMETRY

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

 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

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

 Ordered Pair  Quadrant PREVIOUS VOCABULARY

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

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

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

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

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

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

 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

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

 Dependent variable  Independent variable PREVIOUS VOCABULARY

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

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

 change in y  Up & down RISE

 change in x  Left to right RUN

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

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

 4 types of slope CORE CONCEPT

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

 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

 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:

 Linear function PREVIOUS VOCABULARY

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

 a group of functions with similar characteristics FAMILY OF FUNCTION

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

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

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

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

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

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

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

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

 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

 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:

 Domain  Range PREVIOUS VOCABULARY

 Absolute value function  Vertex  Vertex form CORE VOCABULARY

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

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

 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