Symmetry Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.

Slides:

Advertisements

Similar presentations

Checking an equation for symmetry

Advertisements

East Los Angeles College Mathematics Enrichment

Transformations of Functions Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.

Transformations of Functions Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.

Graphing Circles Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.

Sullivan Algebra and Trigonometry: Section 2.2 Graphs of Equations Objectives Graph Equations by Plotting Points Find Intercepts from a Graph Find Intercepts.

Rectangular Coordinate System

8.2 Symmetry Graphing Nonlinear Equations BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 y-axis Symmetry (figure a) A line or curve drawn on.

Symmetry Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.

1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.

Graphing Circles Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.

Symmetries of Graphs of Equations in x and y

Transformations of Functions Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.

Vertical Stretching or Shrinking of the Graph of a Function Suppose that a > 0. If a point (x, y) lies on the graph of y =  (x), then the point.

Symmetry of Functions Even, Odd, or Neither?. Even Functions All exponents are even. May contain a constant. f(x) = f(-x) Symmetric about the y-axis.

Copyright © 2013, 2009, 2005 Pearson Education, Inc.

Chapter 2.6 Graphing Techniques. One of the main objectives of this course is to recognize and learn to graph various functions. Graphing techniques presented.

Chapter 3: Transformations of Graphs and Data Lesson 4: Symmetries of Graphs Mrs. Parziale.

Section 2.3 Properties of Functions. For an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph.

Symmetry Figures are identical upon an operation Reflection Mirror Line of symmetry.

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.

1.3 Symmetry; Graphing Key Equations; Circles

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

Symmetry and Coordinate Graphs

Section 1.2 Graphs of Equations in Two Variables.

3-1 Symmetry & Coordinate Graphs Objective: 1. To determine symmetry of a graph using algebraic tests. 2. To determine if a function is even or odd.

Symmetry Two points, P and P ₁, are symmetric with respect to line l when they are the same distance from l, measured along a perpendicular line to l.

3-1 Symmetry and Coordinate Graphs. Graphs with Symmetry.

Determine if the following point is on the graph of the equation. 2x – y = 6; (2, 3) Step 1: Plug the given points into the given equation. 2(2) – (3)

Reflection Yes No. Reflection Yes No Line Symmetry.

SYMMETRY, EVEN AND ODD FUNCTIONS NOTES: 9/11. SYMMETRY, EVEN AND ODD FUNCTIONS A graph is symmetric if it can be reflected over a line and remain unchanged.

Test an Equation for Symmetry Graph Key Equations Section 1.2.

TH EDITION LIAL HORNSBY SCHNEIDER COLLEGE ALGEBRA.

Transformations of Functions Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.

0-2: Smart Graphing Objectives: Identify symmetrical graphs

END BEHAVIOR & SYMMETRY Objective: describe the end behavior of a function; determine whether a function is “even, odd, or neither” How do the exponents.

Section 1.2 Graphs of Equations In Two Variables; Intercepts; Symmetry.

Notes Over 1.1 Checking for Symmetry Check for symmetry with respect to both axis and the origin. To check for y-axis symmetry replace x with  x. Sym.

4.3 Symmetry Objective To reflect graphs and use symmetry to sketch graphs. Be able to test equations for symmetry. Use equations to describe reflections.

Objective: SWBAT review graphing techniques of stretching & shrinking, reflecting, symmetry and translations.

AIM: What is symmetry? What are even and odd functions? Do Now : Find the x and y intercepts 1)y = x² + 3x 2) x = y² - 4 (3x + 1)² HW #3 – page 9 (#11-17,

P.1 Graphs and Models Main Ideas Sketch the graph of an equation. find the intercepts of a graph. Test a graph for symmetry with respect to an axis and.

Transformations of Functions

2.1Intercepts;Symmetry;Graphing Key Equations

2.2 Graphs of Equations.

Section 3.5 – Transformation of Functions

Objective: Test for symmetry in polar equations.

How To Graph Quadratic Equations Standard Form.

Graphs of Equations In Two Variables; Intercepts; Symmetry

1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.

How to Graph Quadratic Equations

Sullivan Algebra and Trigonometry: Section 2.2

How To Graph Quadratic Equations

Unit 2: Functions.

East Los Angeles College Mathematics Enrichment

East Los Angeles College Mathematics Enrichment

Chapter 3 – The Nature of Graphs

How To Graph Quadratic Equations.

Unit 2: Functions.

Graphs of Equations Objectives: Find intercepts from a Graph

1.3 Symmetry; Graphing Key Equations; Circles

Worksheet KEY 1) {0, 2} 2) {–1/2} 3) No 4) Yes 5) 6) 7) k = 1 8)

Graphing Absolute Value Functions

How To Graph Quadratic Equations.

Graphs of Equations Objectives: Find intercepts from a Graph

Graphing Key Equations

How To Graph Quadratic Equations.

Presentation transcript:

Symmetry Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology

Symmetric with Respect to the y-Axis A graph that is symmetric to the y-axis, can be seen as slicing a figure vertically. In other words, for every point (x,y) on the graph, the point (-x,y) is also on the graph.

The figure illustrates symmetric with respect to the y-axis. The part of the graph to the right of the y-axis is a reflection (mirror image) of the part to the left of the y-axis.

The following figures illustrate symmetric with respect to the y-axis

Testing for Symmetry with respect to the y-axis Substitute -x for every x in the equation. If the equation is EXACTLY as the original equation, the graph is symmetric with respect to the y-axis.

Testing for Symmetry with respect to the y-axis The following equation is given: Substitute –x for every x. Since the equation is EXACTLY the same as the original equation, then the graph is symmetric with respect to the y-axis.

Is the following equation symmetric with respect to the y-axis?

After substituting a –x for every x, the equation is EXACTLY the same as the original. Therefore, the equation is symmetric with respect to the y-axis.

Is the following equation symmetric with respect to the y-axis?

After substituting a –x for every x, the equation is NOT EXACTLY the same as the original. Therefore, the equation is NOT symmetric with respect to the y-axis.

Is the following equation symmetric with respect to the y-axis?

After substituting a –x for every x, the equation is NOT EXACTLY the same as the original. Therefore, the equation is NOT symmetric with respect to the y-axis.

The function could also be graphed to show that it is NOT symmetric with respect to the y- axis.

Is the following equation symmetric with respect to the y-axis?

After substituting a –x for every x, the equation is EXACTLY the same as the original. Therefore, the equation is symmetric with respect to the y-axis.

The function could also be graphed to show that it is symmetric with respect to the y- axis.

Congratulations!! You just completed symmetric with respect to the y-axis