Section 2.4. X-axis: replace y with –y. Simplify. If you get an equation = to what you started with, the function is symmetric to the x-axis. Y-axis:

Slides:

Advertisements

Similar presentations

Checking an equation for symmetry

Advertisements

Trigonometric Identities Section 4.3. Objectives Use algebra to simplify trigonometric expressions Establish identities.

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

Graphing Equations: Point-Plotting, Intercepts, and Symmetry

Graphs & Models (P1) September 5th, I. The Graph of an Equation Ex. 1: Sketch the graph of y = (x - 1)

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

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 1.2 Graphs of Equations In Two Variables; Intercepts; Symmetry.

2.2 Graphs of Equations in Two Variables Chapter 2 Section 2: Graphs of Equations in Two Variables In this section, we will… Determine if a given ordered.

Section 6.4 Use point plotting to graph polar equations.

Symmetries of Graphs of Equations in x and y

Symmetry in Graphs of Polar Equations On to Sec. 6.5a!!!

Section 1.7 Symmetry & Transformations

Distance and Midpoint Graphing, Symmetry, Circles Solving.

Determine whether a graph is symmetric with respect to the x-axis, the y-axis, and the origin. Determine whether a function is even, odd, or neither even.

Section 6-5 symmetry for polar graphs analyzing a polar graph finding maximum r-values rose curves limaçon curves other polar graphs.

Symmetry and Coordinate Graphs Symmetry and Coordinate Graphs Section 3-1 How do we determine symmetry using algebra? How do we classify functions as even.

2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)

Intercepts y-intercept: where the graph crosses the y-axis. Algebraically – set x=0 x-intercept: where the graph crosses the x-axis. Algebraically – Set.

Copyright © 2009 Pearson Education, Inc. CHAPTER 2: More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra.

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.

FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

S ECTION Graphs of Equations. T HE F UNDAMENTAL G RAPHING P RINCIPLE The graph of an equation is the set of points which satisfy the equation. That.

HPC 1.3 Notes Learning Targets: - Test an equation for symmetry with respect to: x-axis, y-axis, or origin - Know how to graph key equations - Write the.

Domains & Ranges I LOVE Parametric Equations Operations of Functions Inverse Functions Difference.

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

3-1 Symmetry and Coordinate Graphs Pre Calc A. Point Symmetry Symmetric about the origin: any point in Quadrant I has a point in Quadrant III (rotate.

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

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2012 Hawkes Learning Systems. All rights reserved. Symmetry of Functions and Equations.

P7 The Cartesian Plane. Quick review of graphing, axes, quadrants, origin, point plotting.

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.

P.3 Circles & Symmetry.

3.5-3 Symmetry, Monotonicity. In some cases, we will have some kind of symmetry in regards to graphs of a function – Symmetry = a specific part or portion.

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.

Pre-calc section 4-3 Reflections and symmetry part II.

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)

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.

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc More on Functions and Their Graphs.

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.

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

Graphs of Equations Objective: To use many methods to sketch the graphs of equations.

Symmetry & Transformations

Warm – up #2. Homework Log Thurs 11/19 Lesson 4 – 2 Learning Objective: To determine symmetry & graph by translation Hw: #403 Pg. 228 #1 – 35 odd.

Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc More on Functions and Their Graphs.

Do now Solve 4x 4 -65x (3, ∞) Write as an inequality Sketch Bound or unbound?

Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc More on Functions and Their Graphs.

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

Equal distance from origin.

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.

Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

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.

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,

Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

1. Function or Not a Function? 2. Write the closed (explicit) model of the sequence: 3, 7, 11, 15, 19.

2.1Intercepts;Symmetry;Graphing Key Equations

2.2 Graphs of Equations.

Or ODD EVEN Functions.

Graphs of Equations In Two Variables; Intercepts; Symmetry

Section 2.4 Symmetry.

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

Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Functions: Even/Odd/Neither

Chapter 2 More on Functions.

Graphing Key Equations

Presentation transcript:

Section 2.4

X-axis: replace y with –y. Simplify. If you get an equation = to what you started with, the function is symmetric to the x-axis. Y-axis: replace x with –x. Simplify. If you get an equation = to what you started with, the function is symmetric to the y-axis. Origin: replace x with –x AND y with –y. Simplify. If you get an equation = to what you started with, the function is symmetric to the origin.

Test for symmetry: y = |x| - 2 X-axis: -y = |x| - 2y = -|x| + 2 This is not the same, so the function is not symmetric to the x-axis. Y-axis: y = |-x| - 2y = |x| - 2 This is the same, so the function is symmetric to the y-axis. Origin: -y = |-x| - 2y = -|x| + 2 This is not the same, so the function is not symmetric to the origin.

Test for symmetry: 5x – 5y = 0 X-axis: no Y-axis: no Origin: yes

A function is EVEN if it is symmetric to the Y-axis. A function is ODD if it is symmetric to the Origin.

Page – 26 and 34 – 48 evens