'Horizontal stretch' diaporamas de présentation

Math 160

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A. Function Transformers

A. Function Transformers. Pre-Calculus 30. PC30.7 Extend understanding of transformations to include functions (given in equation or graph form) in general, including horizontal and vertical translations, and horizontal and vertical stretches. PC30.8

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7.6 Graphs of the Sine and Cosine Functions 7.8 Phase shift; Sinusoidal Curve Fitting

7.6 Graphs of the Sine and Cosine Functions 7.8 Phase shift; Sinusoidal Curve Fitting. In these sections, we will study the following topics: The graphs of basic sine and cosine functions The amplitude and period of sine and cosine functions Transformations of sine and cosine functions

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Lesson 1-6, page 194

Lesson 1-6, page 194. Symmetry & Transformations. 1.6 Transformation of Functions. Recognize graphs of common functions Use vertical shifts to graph functions Use horizontal shifts to graph functions Use reflections to graph functions Use vertical stretching & shrinking to graph functions

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Vertical and horizontal shifts

Vertical and horizontal shifts. If f is the function y = f(x) = x 2 , then we can plot points and draw its graph as: If we add 1 (outside change) to f(x), we have y = f(x) + 1 = x 2 + 1. We simply take the graph above and move it up 1 unit to get the new graph. y. x. y. (2,5). x.

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Turn homework into the box-staple together and make sure both names are on sheet!! Sckett

Turn homework into the box-staple together and make sure both names are on sheet!! Sckett. Transformation of Functions. Linear Function f(x) = x. The squaring function . The absolute value function . Absolute value- distance from zero for order of operations works like ( ).

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Chapter 3: Functions and Graphs Section 3.4: Graphs and Transformations

Chapter 3: Functions and Graphs Section 3.4: Graphs and Transformations. Essential Question: In the equation g(x) = c[a(x-b)] + d what do each of the letters do to the graph?. 3.4: Graphs and Transformations.

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3.4 Graphs and Transformations

3.4 Graphs and Transformations. Define parent functions. Transform graphs of parent functions. Parent Functions. Parent functions are used to illustrate the basic shape and characteristics of various functions. The rules of transforming these functions can be applied to ANY function.

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September 27 th

Friday, November 1 st. Warm-Up. Write a new equation g(x) compared to f(x) = 4x + 2 Shift up 8 Shift left 6. September 27 th. Match the Equation to the Translation. G(x) = 2x - 4 g(x )=2x -8 g (x )= 2(x+5)-4 g (x)=2x + 8 g(x )=2(x-4) - 6. Shift up 4 units

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September 27 th

Thursday, November 14 th. Warm-Up. Write a new equation g(x) compared to f(x) = 1/2x + 2 Shift up 7 Shift left 4. September 27 th. Homework Answers. What has changed?! . F(x). G(x). Part II-Transformations. Stretches & Compressions .

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Reflections, Transformations and Interval Notation

Reflections, Transformations and Interval Notation. L. Waihman Revised 2006. Reflections of. The graph of is the reflection of the graph of over the x-axis. The graph of is the reflection of the graph of over the y-axis.

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Graphing the Reciprocal Functions

Graphing the Reciprocal Functions. Students will graph the reciprocal trigonometric functions using transformations. Students will write equations of the reciprocal trigonometric functions. HW Review. Reciprocal of cosine Vertical Stretch by 2 Vertical Shift down 3 Horizontal Stretch by 4

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Chapter 3: Transformations of Graphs and Data

Chapter 3: Transformations of Graphs and Data. Lesson 5: The Graph Scale-Change Theorem Mrs. Parziale. Vocabulary:. Vertical stretch : A scale change that makes the original graph taller or shorter Horizontal stretch : a scale change that makes the original graph wider or skinnier.

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1.6 Trig Functions

Photo by Vickie Kelly, 2008. Greg Kelly, Hanford High School, Richland, Washington. 1.6 Trig Functions. Black Canyon of the Gunnison National Park, Colorado.

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Horizontal Stretches and Compression

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Topic: Piecewise-defined Functions section 2.5 part 1 Unit: Graphing Functions

Topic: Piecewise-defined Functions section 2.5 part 1 Unit: Graphing Functions. Teacher: Hedy Cohen Course:Math Analysis Period: 4a, 4b Date: October 22, 2012 Resources: Precalculus with Limits 5 th edition. Warm-up:

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Transformations of graphs

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LEARNING GOALS FOR LESSON 2.9

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Section 1.3

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LEARNING GOALS FOR LESSON 2.6

LEARNING GOALS FOR LESSON 2.6. Recognize sketch and write transformations of linear functions including (1) translation, (2) reflection, (3) stretch/compression and (4) combination of transformations. Example 1: Translating & Reflecting Linear Functions.

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