Monday April 7, 2014 Bell Ringer: Hint: Find the volume of the cone 1 st. Use this volume to work “backwards” to find the radius of the sphere.

Slides:



Advertisements
Similar presentations
Volumes. Right Cylinder Volume of a Right Cylinder (Slices) Cross section is a right circular cylinder with volume Also obtained as a solid of revolution.
Advertisements

Find the volume when the region enclosed by y = x and y = x 2 is rotated about the x-axis? - creates a horn shaped cone - area of the cone will be the.
Notes Over 6.4 Graph Sine, Cosine Functions Notes Over 6.4 Graph Sine, Cosine, and Tangent Functions Equation of a Sine Function Amplitude Period Complete.
Math 10F Transformational Geometry Examples. Translations Translations are “slides” Described by a length and direction Eg. translate the following shape.
Rotation Reflection Translation.
What are we going to do? CFU Learning Objective Activate Prior Knowledge Standard 7.G.1 Verify experimentally the properties of Transformations 2. Our.
A solid of revolution is a solid obtained by rotating a region in the plane about an axis. The sphere and right circular cone are familiar examples of.
Transformation of Functions Section 1.6. Objectives Describe a transformed function given by an equation in words. Given a transformed common function,
Lesson 5-8 Graphing Absolute Value Functions
CN College Algebra Ch. 2 Functions and Their Graphs 2.5: Graphing Techniques: Transformations Goals: Graph functions using horizontal and vertical shifts.
Table of Contents Functions: Transformations of Graphs Vertical Translation: The graph of f(x) + k appears.
Section 3.2 Notes Writing the equation of a function given the transformations to a parent function.
Transformations xf(x) Domain: Range:. Transformations Vertical Shifts (or Slides) moves the graph of f(x) up k units. (add k to all of the y-values) moves.
Geometry Never, never, never give up. Winston Churchill Today:  9.4 Instruction  Practice.
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.
Transformations to Parent Functions. Translation (Shift) A vertical translation is made on a function by adding or subtracting a number to the function.
Transformations We are going to look at some transformation rules today:
Unit 5 – Linear Functions
Geometry Lesson 6.2B – Reflections and Rotations
6-8 Graphing Radical Functions
2.7 Graphing Absolute Value Functions The absolute value function always makes a ‘V’ shape graph.
Graphing Reciprocal Functions
Section 9.5. Composition of Transformations When two or more transformations are combined to form a single transformation, the result is a composition.
Families of Functions Objective: I can understand transformations of functions. Write in your notebook ONLY what you see in the yellow boxes [except for.
Transformations SOL 7.8. Vocabulary Horizontal Axis Horizontal Axis: x-axis Vertical Axis Vertical Axis: y-axis Origin Origin: intersection of the y-axis.
Notes Over 2.4 Graphs of Common Functions Be Familiar with These Common Functions.
TRANSFORMATIONS Shifts Stretches And Reflections.
Sullivan PreCalculus Section 2.5 Graphing Techniques: Transformations
3.4 Graphing Techniques; Transformations. (0, 0) (1, 1) (2, 4) (0, 2) (1, 3) (2, 6)
3-2 Families of Graphs Pre Calc A. Parent Graphs.
Transformation of Functions
Graphical Transformations. Quick Review What you’ll learn about Transformations Vertical and Horizontal Translations Reflections Across Axes Vertical.
Objectives: Explore features of the absolute-value function. Explore basic transformations of the absolute-value function. Standards Addressed: O:
WHICH TRANSFORMATIONS DO YOU KNOW? ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? ROTATION.
 How would you sketch the following graph? ◦ y = 2(x – 3) 2 – 8  You need to perform transformations to the graph of y = x 2  Take it one step at a.
8.2 Area of a Surface of Revolution
Section 3.5 Graphing Techniques: Transformations.
MCR 3U SECTION 3.4 REFLECTIONS OF FUNCTIONS. Example 1: Graph the functions and on a single grid.
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.
9-2 Reflections Objective: To find reflection images of figures.
2.5 Shifting, Reflecting, and Stretching Graphs. Shifting Graphs Digital Lesson.
1.3 Combining Transformations
Objective: I can understand transformations of functions.
1-7 transformations on the coordinate plane
2.7 – Use of Absolute Value Functions and Transformations.
Review of Transformations and Graphing Absolute Value
Section 5.1 The Natural Logarithmic Function: Differentiation.
Vocabulary The distance to 0 on the number line. Absolute value 1.9Graph Absolute Value Functions Transformations of the parent function f (x) = |x|.
I. There are 4 basic transformations for a function f(x). y = A f (Bx + C) + D A) f(x) + D (moves the graph + ↑ and – ↓) B) A f(x) 1) If | A | > 1 then.
1. g(x) = -x g(x) = x 2 – 2 3. g(x)= 2 – 0.2x 4. g(x) = 2|x| – 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1.
The Coordinate Plane SWBAT identify the four quadrants; identify and graph points in all four quadrants.
Section 9.3 Day 1 Transformations of Quadratic Functions
Section 1.4 Transformations and Operations on Functions.
Notes Over 14.2 Translations of Trigonometric Graphs Translation of a Sine Function Amplitude Period.
1. 2 Translations Stretches Reflections Combinations 1. Function Transformations Horizontal Vertical x-axis y-axis y = x Inverse Relations FRSTFRST 3.
Warm Up. True or False? 1.A reflection preserves angle measure. 2.A reflection preserves segment length. 3.A reflection preserves orientation. False True.
Pre-Cal Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations.
Section 2.5 Transformations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
Warm-Up Evaluate each expression for x = -2. 1) (x – 6) 2 4 minutes 2) x ) 7x 2 4) (7x) 2 5) -x 2 6) (-x) 2 7) -3x ) -(3x – 1) 2.
Section 1-5 Graphical Transformations. Section 1-5 vertical and horizontal translations vertical and horizontal translations reflections across the axes.
© The Visual Classroom 3.7 Transformation of Functions Given y = f(x), we will investigate the function y = af [k(x – p)] + q for different values of a,
5-3 Using Transformations to Graph Quadratic Functions.
Transforming Linear Functions
6.03. Do Now – Translate! The position of a box of cookies on a table is represented by the points (-2, 4) (-3, -1) (0, -2) and (1, 3). If the box is.
2D - GEOMETRY POSITIONS ON THE GRID TRANSLATIONS REFLECTIONS ROTATIONS
2.7 Graphing Absolute Value Functions
2.7 Graphing Absolute Value Functions
Transformations Review
15 – Transformations of Functions Calculator Required
Presentation transcript:

Monday April 7, 2014 Bell Ringer: Hint: Find the volume of the cone 1 st. Use this volume to work “backwards” to find the radius of the sphere.

What We are Learning Today: To utilize transformation patterns to obtain new ordered pairs BEFORE graphing To use points obtained from transformation patterns to graph a transformation

First Some Definitions: Rotation: Counter Clock Wise Clock Wise Reflection: Translation: Horizontal: Vertical:

Example: (2, 3) (4, 1) (9, 2) (5, 6) Reflect over y-axis Rotate 90° ccw Translate HORIZONTAL +3 Translate VERTICAL -3

Set 1: (7, 2) (7, 5) (8, 5) (9, 3) Rotate 90° ccw

Set 2: (7, 2) (7, 5) (8, 5) (9, 3) Rotate 180°

Set 3: (7, 2) (7, 5) (8, 5) (9, 3) Rotate 90° cw

Set 4: (7, 2) (7, 5) (8, 5) (9, 3) Reflect y-axis

Set 5: (7, 2) (7, 5) (8, 5) (9, 3) Reflect x-axis

Set 6: (7, 2) (7, 5) (8, 5) (9, 3) Reflect y = x

Set 7: (7, 2) (7, 5) (8, 5) (9, 3) Reflect y = -x

Set 8: (7, 2) (7, 5) (8, 5) (9, 3) Translate HORIZONTALY +3

Set 9: (7, 2) (7, 5) (8, 5) (9, 3) Translate HORIZONTALY -7

Set 10: (7, 2) (7, 5) (8, 5) (9, 3) Translate VERTICALY +4

Set 11: (7, 2) (7, 5) (8, 5) (9, 3) Translate VERTICALY -8