COMPOSITIONS WITH TRANSFORMATIONS. COMPOSITIONS Definition: The nesting of two or more processes to form a single new rule. Composition of Transformations.

Slides:

Advertisements

Similar presentations

Rotation Reflection Translation.

Advertisements

Further Pure 1 Transformations. 2 × 2 matrices can be used to describe transformations in a 2-d plane. Before we look at this we are going to look at.

 Pre-Calculus 30.  PC30.7 PC30.7  Extend understanding of transformations to include functions (given in equation or graph form) in general, including.

Reflections. What will we accomplish in today’s lesson? Given a pre-image and its reflected image, determine the line of reflection. Given a pre-image.

 Reflection: a transformation that uses a line to reflect an image.  A reflection is an isometry, but its orientation changes from the preimage to the.

1 The graphs of many functions are transformations of the graphs of very basic functions. The graph of y = –x 2 is the reflection of the graph of y = x.

Reflections 30 Reflect across y=x (x,y)  (y,x) Reflect across x-axis (x,y)  (x,-y) Reflect across y-axis (x,y)  (-x,y) Reflect across y=x Reflect across.

Transformation a change of position, shape or size of a figure Three types of transformation A slide called a translation A flip, called a reflection The.

Sections 1.8/1.9: Linear Transformations

Polygons and Transformations Unit 2. Essential Questions 1.) How can you change a figure’s position without changing its size and shape? 2.) What process.

Reflections Section 9.3.

Lesson 9.9 Line Reflections and Symmetry. Line of Symmetry Divides the figure in two congruent halves.

Lesson 11.4 Translations and Reflections

Rigid Motion in a Plane 7.1.

Rigid Motion in a Plane Translations and Reflections Glide Reflections

Month Rent Revenue 0 $400.00$ $410.00$ $420.00$

© Daniel Holloway. Transforming graphs is not too dissimilar from transforming shapes. Whereas you can translate, rotate, reflect and enlarge shapes;

1.2: Functions and Graphs. Relation- for each x value, there can be any y-values. Doesn’t pass the VLT. (ex. (1,2), (2,4), (1,-3) Function- For each x-value,

Graphing Reciprocal Functions

3.1 Symmetry; Graphing Key Equations. Symmetry A graph is said to be symmetric with respect to the x-axis if for every point (x,y) on the graph, the point.

Symmetry Smoke and mirrors. Types of Symmetry  X-axis symmetry  Y-axis symmetry  Origin symmetry.

Transformations Day 1: Graphing. Vocabulary Transformations – mapping of a figure on the coordinate plane. 1) Reflection: Mirror image x-axis (x,y) →(x,-y)

(7.1 & 7.2) NOTES- Exponential Growth and Decay. Definition: Consider the exponential function: if 0 < a < 1: exponential decay if a > 1: exponential.

Section 9.5. Composition of Transformations When two or more transformations are combined to form a single transformation, the result is a composition.

Geometry Glide Reflections and Compositions. Goals Identify glide reflections in the plane. Represent transformations as compositions of simpler transformations.

Parabola. Examples Give four examples of equations of parabola all having the vertex (2,3), but one is facing upward, one downward, one to the right.

Bell Work (Have out 7.4s) Sketch a triangle with vertices A (-1, -3), B (1, -1), C (-1, 0). Then sketch the image of the triangle after the translation.

Transformations **Moving a point on a coordinate plane.

4.2 Reflections.

Objective: Students will graph and name ordered pairs (11-7).

Notes Over 2.4 Graphs of Common Functions Be Familiar with These Common Functions.

Reflections Grade 6 Copyright © Ed2Net Learning Inc.1.

Transformations Translation Reflection Rotation Dilation.

Section 3.5 Graphing Techniques: Transformations.

Properties or Rules of Transformations Equations used to find new locations.

EQ: How can transformations effect the graph a parent function? I will describe how transformations effect the graph of a parent function.

1.8 Glide Reflections and Compositions Warm Up Determine the coordinates of the image of P(4, –7) under each transformation. 1. a translation 3 units left.

Aim: Transformation: Translation, Rotation, Dilation Course: Alg. 2 & Trig. Do Now: Reflect ΔCDE through the line y = -2. Aim: How do we move from here.

Topic 2 Summary Transformations.

 2.3: Reflections. What is a Reflection?  Reflection or flip is a transformation in which a figure is reflected on a line called the line of reflection.

Unit 7.5: Shear A transformation that changes the shape but not the size of the figure.

Section 1.4 Transformations and Operations on Functions.

Unit 10 Transformations. Lesson 10.1 Dilations Lesson 10.1 Objectives Define transformation (G3.1.1) Differentiate between types of transformations (G3.1.2)

DRILL 1) If A is in between points B and C and AC is 4x + 12 and AB is 3x – 4 and BC is 57 feet how long is AB? 2) Angles A and B are Supplementary if.

TIME will be on the x-axis. (time is always on the x-axis no matter what!) The number of COOKIES will be on the y-axis. Let’s.

Warm Up Week 1. Section 7.2 Day 1 I will identify and use reflections in a plane. Ex 1 Line of Reflection The mirror in the transformation.

Perform Congruence Transformations. Transformations: when you move or change a geometric figure in some way to produce a new figure. Image is what the.

Types of Rigid Motion Translation Rotation Reflection Objective - To describe and interpret translations and reflections in the coordinate plane.

Linear Algebra Tuesday September 2. Answers for homework.

Transformations Unit 7.

Jan. 17 HW 36: Transformations Day 1 Aim: Working with Dilation & Reflection Materials you will need for this homework: pencil ruler.

Warm up What are my new coordinates after this transformation? (4,6) (-2, 5) (2, 1)  ( x -2, y + 4) Give an example is coordinate notation for the following:

1. 2 Translations Stretches Reflections Combinations 1. Function Transformations Horizontal Vertical x-axis y-axis y = x Inverse Relations FRSTFRST 3.

Pre-Cal Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations.

 coordinate plane  x-axis  y-axis  origin  quadrants  ordered pair  x-coordinate  y-coordinate.

Unit 5 Transformations in the Coordinate Plane. Translations.

1.5 Graphical Transformations Represent translations algebraically and graphically.

Compositions of Transformations. Review Name the Transformation Original Image Translation.

Warm up Reflect the figure ABCD across the line y=x. List the new coordinates of the points A’B’C’D’.

Properties or Rules of Transformations

Transformations Day 2: Composition.

9-2: Translations.

Tuesday, June 22, Reflections 11.3 Reflections

Presentation transcript:

COMPOSITIONS WITH TRANSFORMATIONS

COMPOSITIONS Definition: The nesting of two or more processes to form a single new rule. Composition of Transformations When two transformations are performed, one following the other. Notation: Perform the transformations from right to left T a,b o r y=x (x,y)

COMPOSITIONS PRACTICE Find the image of A(3,-2) under the given compositions. R 90° ∘ r x-axis r x-axis (3, -2) => (3, 2) R 90° (3, 2) => (-2, 3)

COMPOSITIONS PRACTICE What happens if we reverse them? Find the image of A(3,-2) under the given compositions. r x-axis ∘ R 90° R 90° (3, -2) => (2, 3) r x-axis (2, 3) => (2, -3)

COMPARE R 90° ∘ r x-axis = (-2, 3) r x-axis ∘ R 90° = (2, -3) ORDER MATTERS!!

FIND THE IMAGE OF A(3,-2) UNDER THE GIVEN COMPOSITIONS. 1.r x-axis ∘ r y-axis 2.r y-axis ∘ r x-axis 3.R 90 ∘ r x-axis 4.r y-axis ∘ R 90 5.T -1,4 ∘ r y=x 6.r y=x ∘ R 90 7.r y-axis ∘ r y=x 8.R 90 ∘ T 3,-2 9.T -2,4 ∘ D D -2 ∘ T -2,4