4.2 Start Thinking. 4.2 Warm Up. 4.2 Cumulative Review Warm Up
|
|
|
- Ralph Carroll
- 5 years ago
- Views:
Transcription
1 . Start Thinking La a ardstick at the base of a mirror. Stand at the end of the ardstick so ou are 3 feet from the mirror. Is our reflection the same distance from the mirror? Eplain wh or wh not. Hold up our right hand. Is our reflection holding up its right hand as well? Eplain wh or wh not.. Warm Up Reflect point P. State the coordinates of P'. 1. P( 5, 3 ); reflection in -ais. P(, 3 ); reflection in -ais 3. P( 1, 5 ); reflection in -ais. P( 1, 1 ); reflection in -ais 5. P (, ); reflection in -ais. P ( 5, 1 ); reflection in -ais. Cumulative Review Warm Up Classif the angle Copright Big Ideas Learning, LLC Geometr Resources b Chapter 115
2 Name Date. Practice A In Eercises 1 3, graph ABC 1. ( ) A 0,, B 1, 3, C, ; -ais. ( ) ( ) A,, B,, C 3, 5 ; -ais A, 1, B 3,, C 1, 1 ; = 3. and its image after a reflection in the given line. In Eercises and 5, graph the polgon and its image after a reflection in the given line.. = 5. = P Q R S P S R Q In Eercises and 7, graph JKL its image after the glide reflection. with vertices J(, 3 ), K(, 1 ), and L( 1, 5) and. Translation: (, ) ( 1, ) 7. Translation: (, ) ( +, 3) Reflection: in the -ais Reflection: in the line = In Eercises and 9, determine the number of lines of smmetr for the figure Find point W on the -ais so that VW XW X (, 1 ). + is a minimum given V (, 3) 11. A line = 3 5 is reflected in = a so that the image is given b = 1 3. What is the value of a? 1. Your friend claims that it is not possible to have a glide reflection if ou have two translations followed b one reflection. Is our friend correct? Eplain our reasoning. and 11 Geometr Copright Big Ideas Learning, LLC Resources b Chapter
3 Name Date. Practice B In Eercises 1 and, graph CDE and its image after a reflection in the given line. 1. C( 3, ), D(, 1 ), E( 0, 5 ); -ais. C 1,, D 1,, E 7, ; = In Eercises 3 and, graph the polgon and its image after a reflection in the given line. 3. -ais. = 1 L K N K N M L M In Eercises 5 and, graph ABC its image after the glide reflection. with vertices A( 1, ), B(, 1 ), and C(, 3) and 5. Translation: (, ) ( +, 1). Translation: (, ) ( 3, + 1) Reflection: in the line = Reflection: in the line = 7. Determine the number of lines of smmetr. Find point P on the -ais so that for the figure. AP + BP is a minimum. B A 9. Is it possible to perform two reflections of an object so that the final image is identical to the original image? If so, give an eample. If not, eplain our reasoning. 10. A triangle undergoes a glide reflection. Is it possible for the sides of the triangle to change length during this process? Eplain our reasoning. 11. Your friend claims that it is not possible to have a glide reflection if ou have one translation followed b two reflections. Is our friend correct? Eplain our reasoning. Copright Big Ideas Learning, LLC Geometr Resources b Chapter 117
4 Name Date. Enrichment and Etension Reflections 1. Reflect points F and G in the -ais. Name the coordinates and connect the points to form a polgon. Give the most specific name for the polgon.. Reflect points F and G in the -ais. Name the coordinates. F(a, c) G(a, b) 3. Reflect the points A and B in the line =. Connect the points to form a polgon. Give the most specific name for the polgon.. Reflect the points A and B in the line =. Connect the points to form a polgon. Give the most specific name for the polgon. A B are The vertices of ABC A,, B 0, 7, and C 1, 3. Reflect ABC in line 1 to obtain ABC. Then reflect ABC in line to obtain B C. Graph triangles ABC and B C. 5. Line 1: = ; Line : = 1. Line 1: = 3; Line : = 5 11 Geometr Copright Big Ideas Learning, LLC Resources b Chapter
5 Name Date. Puzzle Time What Tpe Of Dance Does A Geometr Teacher Like? Circle the letter of each correct answer in the boes below. The circled letters will spell out the answer to the riddle. Complete the sentence. 1. A is a transformation that uses a line like a mirror to reflect the figure.. If ( a, b) is reflected in the -ais, then its image is the point. 3. If (, ) a b is reflected in the line =, then its image is the point.. A reflection is a transformation involving a translation followed b a reflection. 5. A figure in the plane has line when the figure can be mapped onto itself b a reflection in a line. How man lines of smmetr does the figure have?. 7.. Identif the vertices of the image created after the reflection in the given line. 9. A( 3, ), B( 5, ); = 10. ( ) ( ) A, 3, B, ; -ais A, 1, B 3, 9 ; = 11. H S K L Q U W I A R E 9 ( b, a ) smmetr slider ( 3, 9) 1,, B 5 (, 3 ), (, ) B G I D F O A D N E C E ( 5, ) 3,, B ( b, a) ( a, b).5 reflection rotation ( 1, ), ( 9, 3) B 1 B (, 5), 3, glide Copright Big Ideas Learning, LLC Geometr Resources b Chapter 119
Plot and connect the points in a coordinate plane to make a polygon. Name the polygon.
. Start Thinking Find at least two objects in each of the following categories: circle, square, triangle, and rectangle (nonsquare). Use a table to compare each object of the same categor in the following
Name Date. using the vector 1, 4. Graph ABC. and its image. + to find the image
_.1 ractice 1. Name the vector and write its component form. K J. The vertices of, 3, 1,, and 0, 1. Translate using the vector 1,. Graph and its image. are ( ) ( ) ( ) 3. Find the component form of the
1.4 Start Thinking. 1.4 Warm Up. 1.4 Cumulative Review Warm Up
. Start Thinking A polgon with three sides is called a triangle. The prefix tri- means three. One object with the prefix tri- is a tripod. Tripods have three legs and are often used to stabilize video
Name Date. In Exercises 1 6, graph the function. Compare the graph to the graph of ( )
Name Date 8. Practice A In Eercises 6, graph the function. Compare the graph to the graph of. g( ) =. h =.5 3. j = 3. g( ) = 3 5. k( ) = 6. n = 0.5 In Eercises 7 9, use a graphing calculator to graph the
Fair Game Review. Chapter 11. Name Date. Reflect the point in (a) the x-axis and (b) the y-axis. 2. ( 2, 4) 1. ( 1, 1 ) 3. ( 3, 3) 4.
Name Date Chapter Fair Game Review Reflect the point in (a) the -ais and (b) the -ais.. (, ). (, ). (, ). (, ) 5. (, ) 6. (, ) Copright Big Ideas Learning, LLC Name Date Chapter Fair Game Review (continued)
Rotate. A bicycle wheel can rotate clockwise or counterclockwise. ACTIVITY: Three Basic Ways to Move Things
. Rotations object in a plane? What are the three basic was to move an Rotate A biccle wheel can rotate clockwise or counterclockwise. 0 0 0 9 9 9 8 8 8 7 6 7 6 7 6 ACTIVITY: Three Basic Was to Move Things
11.6 Start Thinking Warm Up Cumulative Review Warm Up
11.6 Start Thinking The diagrams show a cube and a pyramid. Each has a square base with an area of 25 square inches and a height of 5 inches. How do the volumes of the two figures compare? Eplain your
5.8 Start Thinking. 5.8 Warm Up. 5.8 Cumulative Review Warm Up
5.8 Start Thinking Use dnamic geometr software to create an ABC in a coordinate plane such that the center of the triangle is the origin. Use the software to manipulate the triangle so it has whole-number
Name Date. Go to BigIdeasMath.com for an interactive tool to investigate this exploration. and those of A BC?
ame Date.3 Rotations For use with Eploration.3 Essential Question How can ou rotate a figure in a coordinate plane? EXPLORTIO: Rotating a Triangle in a oordinate Plane Go to igideasath.com for an interactive
ACTIVITY 9. Learning Targets: 112 SpringBoard Mathematics Geometry, Unit 2 Transformations, Triangles, and Quadrilaterals. Reflection.
Learning Targets: Perform reflections on and off the coordinate plane. Identif reflectional smmetr in plane figures. SUGGESTED LERNING STRTEGIES: Visualization, Create Representations, Predict and Confirm,
9 3 Rotations 9 4 Symmetry
h 9: Transformations 9 1 Translations 9 Reflections 9 3 Rotations 9 Smmetr 9 1 Translations: Focused Learning Target: I will be able to Identif Isometries. Find translation images of figures. Vocabular:
ACTIVITY: Frieze Patterns and Reflections. a. Is the frieze pattern a reflection of itself when folded horizontally? Explain.
. Reflections frieze pattern? How can ou use reflections to classif a Reflection When ou look at a mountain b a lake, ou can see the reflection, or mirror image, of the mountain in the lake. If ou fold
9.55 in. containers have the same surface area as the ball? If not, which container has a surface area that is closer to that of the ball?
11.8 Start Thinking You buy a friend a basketball as a gift. You want to construct a container to put the ball in to disguise it when it is wrapped. You construct the two containers shown in the diagram.
Translations, Reflections, and Rotations
Translations, Reflections, and Rotations The Marching Cougars Lesson 9-1 Transformations Learning Targets: Perform transformations on and off the coordinate plane. Identif characteristics of transformations
Rotations. Essential Question How can you rotate a figure in a coordinate plane?
11.3 Rotations Essential Question How can ou rotate a figure in a coordinate plane? Rotating a Triangle in a oordinate lane ONSTRUTING VILE RGUMENTS To be proficient in math, ou need to use previousl established
12.1. Angle Relationships. Identifying Complementary, Supplementary Angles. Goal: Classify special pairs of angles. Vocabulary. Complementary. angles.
. Angle Relationships Goal: Classif special pairs of angles. Vocabular Complementar angles: Supplementar angles: Vertical angles: Eample Identifing Complementar, Supplementar Angles In quadrilateral PQRS,
Think About. Unit 5 Lesson 3. Investigation. This Situation. Name: a Where do you think the origin of a coordinate system was placed in creating this
Think About This Situation Unit 5 Lesson 3 Investigation 1 Name: Eamine how the sequence of images changes from frame to frame. a Where do ou think the origin of a coordinate sstem was placed in creating
Chapter 4. Geometry Resources by Chapter. Copyright Big Ideas Learning, LLC All rights reserved.
Chapter Famil and Communit Involvement (English)... 108 Famil and Communit Involvement (Spanish)... 109 Section.1... 110 Section.... 115 Section.3... 10 Section.... 15 Section.5... 130 Section.6... 135
Test, Form 1A. 1. Find the coordinates of J'. A. ( 2, 4) B. ( 2, 4) C. ( 4, 2) D. ( 4, 2)
Chapter Test, Form 1A Write the letter for the correct answer in the blank at the right of each question. For Eercises 1 4, parallelogram JKLM has vertices as shown. Parallelogram JKLM is translated 2
A rotation is a transformation that turns a figure around a point, called the.
Name: # Geometr: Period Ms. Pierre Date: Rotations Toda s Objective KWBAT represent a rotation as a function of coordinate pairs and rotate a figure in the plane following a rule described in words or
Name Date. Congruence and Transformations For use with Exploration 4.4
Nae Date. Congruence and Transforations For use with Eploration. Essential Question What conjectures can ou ae about a figure reflected in two lines? 1 EXLORTION: Reflections in arallel Lines Go to igideasmath.co
9.7 Investigate Dilations
Investigating g eometr ONSTUTION Use before Lesson 9.7 9.7 Investigate Dilations M T E I LS straightedge compass ruler Q U E S T I O N How do ou construct a dilation of a figure? ecall from Lesson 6.7
Isometry: When the preimage and image are congruent. It is a motion that preserves the size and shape of the image as it is transformed.
Chapter Notes Notes #36: Translations and Smmetr (Sections.1,.) Transformation: A transformation of a geometric figure is a change in its position, shape or size. Preimage: The original figure. Image:
How can you enlarge or reduce a figure in the coordinate plane? Dilate. ACTIVITY: Comparing Triangles in a Coordinate Plane.
. Dilations How can ou enlarge or reduce a figure in the coordinate plane? Dilate When ou have our ees checked, the optometrist sometimes dilates one or both of the pupils of our ees. ACTIVITY: Comparing
L3 Rigid Motion Transformations 3.1 Sequences of Transformations Per Date
3.1 Sequences of Transformations Per Date Pre-Assessment Which of the following could represent a translation using the rule T (, ) = (, + 4), followed b a reflection over the given line? (The pre-image
Grade 6 Math Circles February 29, D Geometry
1 Universit of Waterloo Facult of Mathematics Centre for Education in Mathematics and Computing Grade 6 Math Circles Feruar 29, 2012 2D Geometr What is Geometr? Geometr is one of the oldest ranches in
The Marching Cougars Lesson 9-1 Transformations
The Marching Cougars Lesson 9-1 Learning Targets: Perform transformations on and off the coordinate plane. Identif characteristics of transformations that are rigid motions and characteristics of transformations
Name Date. In Exercises 1 and 2, find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.
Name ate. ractice In Eercises 1 and, find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 1.. 9 7 10 In Eercises 3, cop the diagram. Then use a compass
Lesson 9.1 Properties of Transformations
Lesson 9.1 roperties of Transformations Name eriod Date In Eercises 1 3, draw the image according to the rule and identif the tpe of transformation. 1. (, ) (, ) 2. (, ) ( 4, 6) 3. (, ) (4, ) 6 4 2 6 4
Graphing f ( x) = ax 2 + c
. Graphing f ( ) = a + c Essential Question How does the value of c affect the graph of f () = a + c? Graphing = a + c Work with a partner. Sketch the graphs of the functions in the same coordinate plane.
Drawing Polygons in the Coordinate Plane
Lesson 7 Drawing Polgons in the Coordinate Plane 6.G. Getting the idea The following points represent the vertices of a polgon. A(, 0), B(0, ), C(, ), D(, ), and E(0, ) To draw the polgon, plot the points
Practice 8-1. Translations. Use arrow notation to write a rule that describes the translation shown on each graph.
ame lass ate Practice 8-1 Translations Use arrow notation to write a rule that describes the translation shown on each graph. 1.. 3. Pearson ducation, Inc., publishing as Pearson Prentice Hall. ll rights
Understanding Reflections
Lesson 18 Understanding Reflections 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G., 8.G.3 1 Getting the idea A reflection is a tpe of transformation in which ou flip a figure across a line called the line of reflection.
3.1 Sequences of Transformations
Name lass Date 3.1 Sequences of Transformations Essential Question: What happens when ou appl more than one transformation to a figure? Eplore ombining Rotations or Reflections transformation is a function
Worksheet on Line Symmetry & Rotational Symmetry
Gr. 9 Math 8. - 8.7 Worksheet on Line Smmetr & Rotational Smmetr Multiple Choice Identif the choice that best completes the statement or answers the question.. Which shapes have at least lines of smmetr?
Practice For use with pages
9. For use with pages 598 605 Use the translation (, ) ( 6, 3).. What is the image of (3, )?. What is the image of (4, )? 3. What is the preimage of 9(, 7)? 4. What is the preimage of 9(3, )? The vertices
Isometries and Congruence
Honors Geometr Section.1 Name: Date: Period: Isometries and Congruence transformation of a geometric figure is a change in its position, shape, or size.. The original figure is called the preimage. The
Mirror, Mirror Reflections of Figures on the
Mirror, Mirror Reflections of Figures on the 4 Coordinate Plane WARM UP Determine each product. 1. 21 3 6 2. 2 3 5 (21) LEARNING GOALS Reflect geometric figures on the coordinate plane. Identif and describe
Perimeter and Area in the Coordinate Plane
1. Perimeter and Area in the Coordinate Plane COMMON CORE Learning Standard HSG-GPE.B.7 HSG-MG.A.1 LOOKING FOR STRUCTURE To be proficient in math, ou need to visualize single objects as being composed
Reteaching Golden Ratio
Name Date Class Golden Ratio INV 11 You have investigated fractals. Now ou will investigate the golden ratio. The Golden Ratio in Line Segments The golden ratio is the irrational number 1 5. c On the line
Half Turns and Quarter Turns Rotations of Figures on the Coordinate Plane
Half Turns and Quarter Turns Rotations of Figures on the Coordinate Plane 5 WARM UP 1. Redraw each given figure as described. a. so that it is turned 10 clockwise Before: After: s D b. so that it is turned
3.5 Write and Graph Equations
.5 Write and Graph Equations of Lines Goal p Find equations of lines. Your Notes VOCABULARY Slope-intercept form Standard form Eample Write an equation of a line from a graph Write an equation of the line
Chapter 9 Transformations
Section 9-1: Reflections SOL: G.2 The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving smmetr and transformation.
COORDINATE ALGEBRA UNIT 5: TRANSFORMATIONS IN THE COORDINATE PLANE. 1. On this coordinate plane, UVW has been transformed to form its image U''V''W''.
1. On this coordinate plane, UVW has been transformed to form its image U''V''W''. 3.Graph the figure and its image under the given translation: EFG with vertices E (-2, -3), F (-3, -2), G (-1, -1) under
37 Pentagon ABCDE is drawn on the grid below.
Pentagon ABCDE is drawn on the grid below. C D E B - - - - - A - - 0 - - - - - - - On the grid, draw a translation of pentagon ABCDE five units down. Be sure to draw the translated shape label the translated
ACTIVITY: Graphing a Linear Equation. 2 x x + 1?
. Graphing Linear Equations How can ou draw its graph? How can ou recognize a linear equation? ACTIVITY: Graphing a Linear Equation Work with a partner. a. Use the equation = + to complete the table. (Choose
Alternate Angles. Clip 67. Mathswatch
Clip 67 Alternate Angles ) Line PQ is parallel to line RS If angle PQR is equal to 6 a) What is the size of angle QRS? b) Give a reason for ou answer. P 6 Q R S ) Line DCE is parallel to line AB a) Find
Time To Hit The Slopes. Exploring Slopes with Similar Triangles
Time To Hit The Slopes Eploring Slopes with Similar Triangles Learning Goals In this lesson, ou will: Use an equation to complete a table of values. Graph an equation using a table of values. Use transformations
4.1 Graph Quadratic Functions in
4. Graph Quadratic Functions in Standard Form Goal p Graph quadratic functions. Your Notes VOCABULARY Quadratic function Parabola Verte Ais of smmetr Minimum and maimum value PARENT FUNCTION FOR QUADRATIC
STRAND I: Geometry and Trigonometry. UNIT 37 Further Transformations: Student Text Contents. Section Reflections. 37.
MEP Jamaica: STRN I UNIT 7 Further Transformations: Student Tet ontents STRN I: Geometr and Trigonometr Unit 7 Further Transformations Student Tet ontents Section 7. Reflections 7. Rotations 7. Translations
Polygons in the Coordinate Plane
. Polgons in the Coordinate Plane How can ou find the lengths of line segments in a coordinate plane? ACTIVITY: Finding Distances on a Map Work with a partner. The coordinate grid shows a portion of a
Putting the V in Absolute Value Defining Absolute Value Functions and Transformations
1 Putting the V in Absolute Value Defining Absolute Value Functions and Transformations Warm Up The graph of f() 5 is shown. Graph each transformation. 1. g() 5 f() 1 5 2. h() 5 2? f() 2 3 Learning Goals
Copyright 2009 Pearson Education, Inc. Chapter 9 Section 5 - Slide 1 AND
Copyright 2009 Pearson Education, Inc. Chapter 9 Section 5 - Slide 1 AND Chapter 9 Geometry Copyright 2009 Pearson Education, Inc. Chapter 9 Section 5 - Slide 2 WHAT YOU WILL LEARN Transformational geometry,
Up, Down, and All Around Transformations of Lines
Up, Down, and All Around Transformations of Lines WARM UP Identif whether the equation represents a proportional or non-proportional relationship. Then state whether the graph of the line will increase
Mirror, Mirror Reflections of Figures on the
Mirror, Mirror Reflections of Figures on the 4 Coordinate Plane WARM UP Determine each product. 1. 21 3 6 2. 2 3 5 (21) LEARNING GOALS Reflect geometric figures on the coordinate plane. Identif and describe
Name: Period: Date: Analyzing Graphs of Functions and Relations Guided Notes
Analzing Graphs of Functions and Relations Guided Notes The graph of a function f is the set of ordered pairs(, f ), in the coordinate plane, such that is the domain of f. the directed distance from the
Developing Conceptual Understanding of Number. Set H: Coordinate Geometry
Developing Conceptual Understanding of Number Set H: Coordinate Geometr Carole Bilk cbilk@gov.mb.ca Wane Watt wwatt@mts.net Vocabular -ais -ais -coordinate -coordinate Notes Coordinate Geometr 1 coordinate
Sequences of Transformations
OMMON ORE D P j E E F F D F k D E Locker LESSON 3.1 Sequences of Transformations Name lass Date 3.1 Sequences of Transformations Essential Question: What happens when ou appl more than one transformation
Graphing f ( x) = ax 2
. Graphing f ( ) = a Essential Question What are some of the characteristics of the graph of a quadratic function of the form f () = a? Graphing Quadratic Functions Work with a partner. Graph each quadratic
Name Date. Modeling with Polynomial Functions For use with Exploration 4.9
4.9 Modeling with Polnomial Functions For use with Eploration 4.9 Essential Question How can ou find a polnomial model for real-life data? 1 EXPLORATION: Modeling Real-Life Data Go to BigIdeasMath.com
Transforming Coordinates
# Transforming Coordinates The drawing window in man computer geometr programs is a coordinate grid. You make designs b specifing the endpoints of line segments. When ou transform a design, the coordinates
5 and Parallel and Perpendicular Lines
Ch 3: Parallel and Perpendicular Lines 3 1 Properties of Parallel Lines 3 Proving Lines Parallel 3 3 Parallel and Perpendicular Lines 3 Parallel Lines and the Triangle Angles Sum Theorem 3 5 The Polgon
To prove theorems using figures in the coordinate plane
6-9 s Using Coordinate Geometr Content Standard G.GPE.4 Use coordinates to prove simple geometric theorems algebraicall. bjective To prove theorems using figures in the coordinate plane Better draw a diagram!
By naming a function f, you can write the function using function notation. Function notation. ACTIVITY: Matching Functions with Their Graphs
5. Function Notation represent a function? How can ou use function notation to B naming a function f, ou can write the function using function notation. f () = Function notation This is read as f of equals
Rational Functions with Removable Discontinuities
Rational Functions with Removable Discontinuities 1. a) Simplif the rational epression and state an values of where the epression is b) Using the simplified epression in part (a), predict the shape for
1) y = 2x 7 2) (-2, 3) ( 3, -1) 3) table. 4) y 5 = ½ ( x 4) 5) 2x + 4y = 7 6) y = 5 7) 8) 9) (-1, 5) (0, 4) 10) y = -3x 7. 11) 2y = -3x 5 12) x = 5
I SPY Slope! Geometr tetbook 3-6, pg 165 (), pg 172 (calculator) Name: Date: _ Period: Strategies: On a graph or a table rise ( Δ) Slope = run Δ ( ) Given 2 points Slope = 2 2 In an equation 1 1 1) = 2
Representations of Transformations
? L E S S N 9.4 Algebraic Representations of Transformations ESSENTIAL QUESTIN Algebraic Representations of Translations The rules shown in the table describe how coordinates change when a figure is translated
9. Tina wants to estimate the heights of two. a) Tina s shadow is 2.4 m and the first tree s. b) Tina s shadow is 0.
b) J 1 15 G F 9. Tina wants to estimate the heights of two trees. For each tree, she stands so that one end of her shadow coincides with one end of the shadow of the tree. Tina s friend measures the lengths
(0, 2) y = x 1 2. y = x (2, 2) y = 2x + 2
.5 Equations of Parallel and Perpendicular Lines COMMON CORE Learning Standards HSG-GPE.B.5 HSG-GPE.B. Essential Question How can ou write an equation of a line that is parallel or perpendicular to a given
Math 1050 Lab Activity: Graphing Transformations
Math 00 Lab Activit: Graphing Transformations Name: We'll focus on quadratic functions to eplore graphing transformations. A quadratic function is a second degree polnomial function. There are two common
Section A Angle Facts Grade F D
Name: Teacher ssessment Section ngle Facts Grade F IN THIS SETION NONE OF THE IGRMS RE RWN URTELY. 1. (a) The diagram shows 3 angles on a straight line. Not drawn accu Work out the value of. 60º 70º º..
1. y = f(x) y = f(x + 3) 3. y = f(x) y = f(x 1) 5. y = 3f(x) 6. y = f(3x) 7. y = f(x) 8. y = f( x) 9. y = f(x 3) + 1
.7 Transformations.7. Eercises To see all of the help resources associated with this section, click OSttS Chapter b. Suppose (, ) is on the graph of = f(). In Eercises - 8, use Theorem.7 to find a point
Transformations. which the book introduces in this chapter. If you shift the graph of y 1 x to the left 2 units and up 3 units, the
CHAPTER 8 Transformations Content Summar In Chapter 8, students continue their work with functions, especiall nonlinear functions, through further stud of function graphs. In particular, the consider three
14-1. Translations. Vocabulary. Lesson
Chapter 1 Lesson 1-1 Translations Vocabular slide, translation preimage translation image congruent figures Adding fied numbers to each of the coordinates of a figure has the effect of sliding or translating
MF9SB_CH08_p pp7.qxd 4/10/09 11:44 AM Page NEL
362 NEL Chapter 8 Smmetr GOLS You will be able to identif and appl line smmetr identif and appl rotation smmetr relate smmetr to transformations solve problems b using diagrams Smmetr is often seen in
Laurie s Notes. Overview of Section 6.3
Overview of Section.3 Introduction In this lesson, eponential equations are defined. Students distinguish between linear and eponential equations, helping to focus on the definition of each. A linear function
Quadratic Inequalities
TEKS FCUS - Quadratic Inequalities VCABULARY TEKS ()(H) Solve quadratic inequalities. TEKS ()(E) Create and use representations to organize, record, and communicate mathematical ideas. Representation a
3-2 Study Guide and Intervention
NAME DATE PERID 3-2 Stud Guide and Intervention Solving Sstems of Inequalities b Graphing Sstems of Inequalities To solve a sstem of inequalities, graph the inequalities in the same coordinate plane. The
9-1. Translations. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
9- Translations Vocabular Review. Underline the correct word to complete the sentence. If two triangles are congruent, corresponding angle measures are the same/ different and corresponding side lengths
Connecting Algebra and Geometry with Polygons
Connecting Algebra and Geometr with Polgons 15 Circles are reall important! Once ou know our wa around a circle, ou can use this knowledge to figure out a lot of other things! 15.1 Name That Triangle!
1.1. Parent Functions and Transformations Essential Question What are the characteristics of some of the basic parent functions?
1.1 Parent Functions and Transformations Essential Question What are the characteristics of some of the basic parent functions? Identifing Basic Parent Functions JUSTIFYING CONCLUSIONS To be proficient
Performing Congruence and Similarity Transformations. C m
9 ig Idea HPTER SUMMRY IG IES Performing ongruence and Similarit Transformations For Your Notebook Translation Translate a figure right or left, up or down. Reflection Reflect a figure in a line. 9 9 9
23.1 Perpendicular Bisectors of Triangles
Name lass Date 3.1 Perpendicular isectors of Triangles Essential Question: How can ou use perpendicular bisectors to find the point that is equidistant from all the vertices of a triangle? Resource Locker
The Graph Scale-Change Theorem
Lesson 3-5 Lesson 3-5 The Graph Scale-Change Theorem Vocabular horizontal and vertical scale change, scale factor size change BIG IDEA The graph of a function can be scaled horizontall, verticall, or in
Parabolas Section 11.1
Conic Sections Parabolas Section 11.1 Verte=(, ) Verte=(, ) Verte=(, ) 1 3 If the equation is =, then the graph opens in the direction. If the equation is =, then the graph opens in the direction. Parabola---
Lesson 7.1 Transformations and Symmetry
Lesson 7.1 ransformations and Smmetr Name eriod Date In Eercises 1 3, perform each transformation. 1. eflect I across line.. otate AL 70 clockwise 3. ranslate ENA b about Q. the given vector. I L A N Q
Geometric Transformations: Translation:
Geometric Transformations: Translation: slide Reflection: Rotation: Dialation: mirror turn enlarge or reduce Notation: Pre-Image: original figure Image: after transformation. Use prime notation C A B C
Essential Question What are the characteristics of the graph of the tangent function?
8.5 Graphing Other Trigonometric Functions Essential Question What are the characteristics of the graph of the tangent function? Graphing the Tangent Function Work with a partner. a. Complete the table
Name Class Date. subtract 3 from each side. w 5z z 5 2 w p - 9 = = 15 + k = 10m. 10. n =
Reteaching Solving Equations To solve an equation that contains a variable, find all of the values of the variable that make the equation true. Use the equalit properties of real numbers and inverse operations
Essential Question How many turning points can the graph of a polynomial function have?
.8 Analzing Graphs of Polnomial Functions Essential Question How man turning points can the graph of a polnomial function have? A turning point of the graph of a polnomial function is a point on the graph
The Graph of an Equation
60_0P0.qd //0 :6 PM Page CHAPTER P Preparation for Calculus Archive Photos Section P. RENÉ DESCARTES (96 60) Descartes made man contributions to philosoph, science, and mathematics. The idea of representing
Pre-Algebra Notes Unit 13: Angle Relationships and Transformations
Pre-Algebra Notes Unit 13: Angle Relationships and Transformations Angle Relationships Sllabus Objectives: (7.1) The student will identif measures of complementar, supplementar, and vertical angles. (7.2)
1.1 Practice B. a. Without graphing, identify the type of function modeled by the equation.
Name Date Name Date. Practice A. Practice B In Exercises and, identif the function famil to which f belongs. Compare the graph of f to the graph of its parent function... x f(x) = x In Exercises and, identif
7.4 Start Thinking. 7.4 Warm Up. 7.4 Cumulative Review Warm Up
7. Start Thinking rhombus and a square are both quadrilaterals with four congruent sides, but a square alwas contains four right angles. Examine the diagrams below and determine some other distinctive
Appendix C: Review of Graphs, Equations, and Inequalities
Appendi C: Review of Graphs, Equations, and Inequalities C. What ou should learn Just as ou can represent real numbers b points on a real number line, ou can represent ordered pairs of real numbers b points
Method 1: Use Pencil and Paper 1. Draw the triangle with vertices A(2, 5), B(1, 2), and C(6, 2). Use the. that it is isosceles.
3. Verif Properties of Triangles Since triangular frames are strong and simple to make, the are widel used to strengthen buildings and other structures. This section applies analtic geometr to verif the
Function Notation. Essential Question How can you use function notation to represent a function?
. Function Notation Essential Question How can ou use function notation to represent a function? The notation f(), called function notation, is another name for. This notation is read as the value of f
Guided Problem Solving
-1 Guided Problem Solving GPS Student Page 57, Exercises 1 1: Match each rule with the correct translation. A. (x, y) (x, y 1 ) I. P(, 1) P (3, ) B. (x, y) (x 1 3, y) II. Q(3, 0) Q (3, ) C. (x, y) (x 1,
Reflecting Any Points on the Coordinate Plane
ACTIVITY 4.2 Reflecting An Points on the Coordinate Plane NOTES Consider the point (, ) located anwhere in the first quadrant. (, ) 0 1. Use the table to record the coordinates of each point. a. Reflect
Unit 5 Lesson 2 Investigation 1
Name: Investigation 1 Modeling Rigid Transformations CPMP-Tools Computer graphics enable designers to model two- and three-dimensional figures and to also easil manipulate those figures. For eample, interior