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: Identify and perform dilations. Solve real-life problems involving scale factors and dilations. 4.5 DILATIONS
What does it mean to dilate a figure? LEAVE 4 LINES ESSENTIAL QUESTION:
dilation center of dilation Scale factor enlargement reduction CORE VOCABULARY
Transformation a figure is enlarged or reduced DILATION
a fixed point about which all points are expanded or reduced CENTER OF DILATION
the ratio of the lengths of the corresponding sides of the image and the preimage SCALE FACTOR
the scale factor k > 1 Figure is enlarged ENLARGEMENT
0 < k < 1 Figure is reduced REDUCTION
Translation Reflection Glide reflection Rotation Dilation CORE CONCEPT: 4 TYPES OF TRANSFORMATIONS
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