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.

Slides:

Advertisements

Similar presentations

Graphing Equations: Point-Plotting, Intercepts, and Symmetry

Advertisements

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.

Coordinate Plane 9/20. TOOLBOX: SUMMARY: Coordinate Plane: x and y-axis used to graph equations Quadrant II (neg, pos) Quadrant I (pos, pos) x-axis Origin.

Section 1.1 The Distance and Midpoint Formulas. x axis y axis origin Rectangular or Cartesian Coordinate System.

3.1 Symmetry & Coordinate Graphs

Symmetries of Graphs of Equations in x and y

Section 1.7 Symmetry & Transformations

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.

“Before Calculus”: New Functions from Old.  Calculus,10/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc.

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

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.

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.

PRECALCULUS Inverse Relations and Functions. If two relations or functions are inverses, one relation contains the point (x, y) and the other relation.

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

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

Symmetry and Coordinate Graphs

Objective: Identify even or odd functions. Warm up a.Describe where is the function increasing, decreasing or constant. b.What is the relative maximum?

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.

3-1 Symmetry. Symmetry All Around Us Symmetry at the Beach Symmetry at the Beach Line Symmetry & Rotational Symmetry - All you need to Know + Symmetry.

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)

Test an Equation for Symmetry Graph Key Equations Section 1.2.

Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.

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

Increasing & Decreasing Functions A function f is increasing on an interval if, for any x 1 and x 2, in the interval, x 1 < x 2 implies f(x 1 ) < f(x 2.

Math 1111 Test #2 Review Fall Find f ° g.

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

Unit 9 Review Find the equation of the axis of symmetry, along with the coordinates of the vertex of the graph and the y-intercept, for the following equation.

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.

Algebra Review Objective: Students will be able to demonstrate their ability to plot points on the Cartesian coordinate system.

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:

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,

Transformationf(x) y = f(x) + c or y = f(x) – c up ‘c’ unitsdown ‘c’ units EX: y = x 2 and y = x F(x)-2 xy F(x) xy

Calculus P - Review Review Problems

1.5 Graphical Transformations Represent translations algebraically and graphically.

Definition: Even Function

2.1Intercepts;Symmetry;Graphing Key Equations

2.2 Graphs of Equations.

3.1 Symmetry and Coordinate Graphs

Graphs of Equations In Two Variables; Intercepts; Symmetry

Symmetry and Coordinate Graphs Section 3-1

Section 2.4 Symmetry.

Unit 2: Functions.

Chapter 3 – The Nature of Graphs

3-4 Inverse Functions and Relations

Graphs of Equations Objectives: Find intercepts from a Graph

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.

Power Functions Investigating symmetry to determine if a power function is even, odd, or neither.

Chapter 2 More on Functions.

Graphs of Equations Objectives: Find intercepts from a Graph

Graphing Key Equations

Classify functions as even or odd.

Odd and Even Functions MCC9-12.F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of.

Properties of Functions

Presentation transcript:

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 180˚)

Determining Point Symmetry Algebraically A function, f(x) is symmetric about the origin if and only if f(-x) = -f(x)

Ex 17: Determine whether each function is symmetric with respect to the origin. a. f(x) = x 6 b. g(x)= -3x 3 + 5x

Line symmetry

Determining Line Symmetry Algebraically For all f(x) when testing for line symmetry the equation must be equal to the original. x-axis: (a, -b)y-axis: (-a, b) y = x: (b, a) y = -x: (-b, -a)

Ex : Determine whether the graph of x² + y = 3 is symmetric with respect to the x-axis, y-axis, y = x, and y = -x

Ex last one: With a partner determine whether the graph of is symmetric to the origin, x-axis, y-axis, y=x, and y = -x.