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.

By: Spencer Weinstein, Mary Yen, Christine Ziegler Respect The Calculus!

7-4 Evaluating and Graphing Sine and Cosine Objective: To use reference angles, calculators or tables, and special angles to find values of the sine and.

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.

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.

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

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

Symmetries of Graphs of Equations in x and y

Section 3.2 Graphs of Equations Objectives: Find the symmetries of equations with respect to x, y axis and origin. Use the graphical interpretation In.

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.

4.3 Reflecting Graphs; Symmetry In this section and the next we will see how the graph of an equation is transformed when the equation is altered. This.

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.

Reflection MCC8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. Picture with.

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

Example: The graph of x = | y | – 2 shown below, is symmetric to x-axis y x 1 2 –323 A graph is symmetric to x- axis if whenever (x, y) is on graph, so.

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.

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.

Sullivan Algebra and Trigonometry: Section 10.2 Objectives of this Section Graph and Identify Polar Equations by Converting to Rectangular Coordinates.

P.1 Graphs and Models. Objectives  Sketch the graph of an equation.  Find the intercepts of a graph.  Test a graph for symmetry with respect to an.

0-2: Smart Graphing Objectives: Identify symmetrical graphs

PRE-ALGEBRA “Symmetry and Reflections” (9-9) A figure has symmetry when one half is a mirror image of the other half (in other words, both halves are congruent).

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.

WARM UP Evaluate 1. and when and 2. and when and.

Transformations of Functions

2.1Intercepts;Symmetry;Graphing Key Equations

Intercepts of a Graph Intercepts are the points at which the graph intersects the x-axis or the y-axis. Since an intercept intersects the x-axis or the.

2.2 Graphs of Equations.

Objective: Test for symmetry in polar equations.

Coefficients a, b, and c are coefficients Examples: Find a, b, and c.

Graphs of Equations In Two Variables; Intercepts; Symmetry

Sullivan Algebra and Trigonometry: Section 2.2

Symmetry and Coordinate Graphs Section 3-1

Notes Over 1.1 To check for y-axis symmetry replace x with -x.

Section 2.4 Symmetry.

East Los Angeles College Mathematics Enrichment

East Los Angeles College Mathematics Enrichment

Chapter 3 – The Nature of Graphs

Intercepts and Symmetry

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)

Intercepts of a Graph Intercepts are the points at which the graph intersects the x-axis or the y-axis. Since an intercept intersects the x-axis or the.

Graphs of Equations Objectives: Find intercepts from a Graph

Graphing Key Equations

Graphing Key Equations

Presentation transcript:

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

Symmetric with Respect to the x-Axis A graph that is symmetric to the x-axis, can be seen as slicing a figure horizontally. 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 x-axis. The part of the graph above the x-axis is a reflection (mirror image) of the part below the x-axis.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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